probability

juantheron · 2011-12-02 01:48:41

Let A = {0,1,2 ..... 9}

how many different 4-digit number that is divisible by 3

if number is choosen from set A

careless25 · 2011-12-02 02:29:07

Are we allowed to choose a number more than once? for eg can we make a 4 digit number: 9999?

And to get you started:

How do you check if a number is divisible by 3?
How many such combinations are there from your set?

John E. Franklin · 2011-12-02 02:36:03

Assume that 0000 = 0 and 0003 = 3 and 0099 = 99 and 0999 = 999.
If this is allowable the answer is:

9999/3 or 3333 I believe.

bobbym · 2011-12-02 07:03:41

Hi;

If we assume with replacement, then there are 9000 numbers(1000 - 9999 ). So there are 3000 numbers that are divisible by 3.

If we assume without replacement, then there are 9*9*8*7=4536 possible 4 digit numbers.
Of those there are 1548 that are divisble by 3.

careless25 · 2011-12-02 07:46:28

If we assume without replacement, then there are 9*9*8*7=4536 possible 4 digit numbers.

I am wondering how you got 9*9 when you say without replacement.
enlighten me!

Edit: Nevermind, I see what assumption you made.

Last edited by careless25 (2011-12-02 07:49:53)

juantheron · 2011-12-04 02:40:48

here we take no. without replacement

thanks to all

bobbym i want more explanation for without replacement

thanks

bobbym · 2011-12-04 05:05:15

To have a 4 digit number you can not have a zero up front so there are 9 choices for the first. There are 9 remaining for the second. Eight choices remaining for the third. And seven left for the fourth.

9 * 9 * 8 * 7 = 4536

reconsideryouranswer · 2011-12-05 05:02:25

juantheron wrote:

Let A = {0,1,2 ..... 9}
how many different 4-digit number that is divisible by 3
if number is choosen from set A

lookagain edit wrote:

Let A = {0,1,2 ..... 9}
How many different 4-digit numbers are divisible by 3
if each digit is chosen without replacement
from set A, and 0 cannot be a leading digit?

For each of the following, there are potentially 4! permutations,
except that 0 cannot be a leading digit, so 3! permutations
must be subtracted. So multiply each of these representative
numbers by 18 to get the total number of permutations for
this partial group:

1023
1026
1029
1035
1038
1047
1053
1056
1062
1065
1068
1074
1083
1086
1089
---------

18(15) = 270

___________________

For this second (last) partial group,
the number of permutations for
each representative number is 4!
Then multiply by 24 to get the total
number of permutations for this
partial group:

1236
1239
1245
1248
1257
1269
1278

1347
1356
1359
1368
1389

1458
1467
1479

1569
1578

1689

2346
2349
2358
2367
2379

2457
2469
2478

2568

2679

3456
3459
3468

3567
3579

3678

3789

4569
4578

5679

6789
--------

24(39) = 936

Grand total
-------------
270 + 936 = 1,206

bobbym · 2011-12-05 06:52:57

Hi;

reconsideryouranswer wrote:

]Grand total
-------------
270 + 936 = 1,206

The answer of 1206 is a little low.

Here they are:

{1023, 1026, 1029, 1032, 1035, 1038, 1047, 1053, 1056, 1059, 1062, \
1065, 1068, 1074, 1083, 1086, 1089, 1092, 1095, 1098, 1203, 1206, \
1209, 1230, 1236, 1239, 1245, 1248, 1254, 1257, 1260, 1263, 1269, \
1275, 1278, 1284, 1287, 1290, 1293, 1296, 1302, 1305, 1308, 1320, \
1326, 1329, 1347, 1350, 1356, 1359, 1362, 1365, 1368, 1374, 1380, \
1386, 1389, 1392, 1395, 1398, 1407, 1425, 1428, 1437, 1452, 1458, \
1467, 1470, 1473, 1476, 1479, 1482, 1485, 1497, 1503, 1506, 1509, \
1524, 1527, 1530, 1536, 1539, 1542, 1548, 1560, 1563, 1569, 1572, \
1578, 1584, 1587, 1590, 1593, 1596, 1602, 1605, 1608, 1620, 1623, \
1629, 1632, 1635, 1638, 1647, 1650, 1653, 1659, 1674, 1680, 1683, \
1689, 1692, 1695, 1698, 1704, 1725, 1728, 1734, 1740, 1743, 1746, \
1749, 1752, 1758, 1764, 1782, 1785, 1794, 1803, 1806, 1809, 1824, \
1827, 1830, 1836, 1839, 1842, 1845, 1854, 1857, 1860, 1863, 1869, \
1872, 1875, 1890, 1893, 1896, 1902, 1905, 1908, 1920, 1923, 1926, \
1932, 1935, 1938, 1947, 1950, 1953, 1956, 1962, 1965, 1968, 1974, \
1980, 1983, 1986, 2013, 2016, 2019, 2031, 2034, 2037, 2043, 2046, \
2049, 2058, 2061, 2064, 2067, 2073, 2076, 2079, 2085, 2091, 2094, \
2097, 2103, 2106, 2109, 2130, 2136, 2139, 2145, 2148, 2154, 2157, \
2160, 2163, 2169, 2175, 2178, 2184, 2187, 2190, 2193, 2196, 2301, \
2304, 2307, 2310, 2316, 2319, 2340, 2346, 2349, 2358, 2361, 2364, \
2367, 2370, 2376, 2379, 2385, 2391, 2394, 2397, 2403, 2406, 2409, \
2415, 2418, 2430, 2436, 2439, 2451, 2457, 2460, 2463, 2469, 2475, \
2478, 2481, 2487, 2490, 2493, 2496, 2508, 2514, 2517, 2538, 2541, \
2547, 2568, 2571, 2574, 2580, 2583, 2586, 2589, 2598, 2601, 2604, \
2607, 2610, 2613, 2619, 2631, 2634, 2637, 2640, 2643, 2649, 2658, \
2670, 2673, 2679, 2685, 2691, 2694, 2697, 2703, 2706, 2709, 2715, \
2718, 2730, 2736, 2739, 2745, 2748, 2751, 2754, 2760, 2763, 2769, \
2781, 2784, 2790, 2793, 2796, 2805, 2814, 2817, 2835, 2841, 2847, \
2850, 2853, 2856, 2859, 2865, 2871, 2874, 2895, 2901, 2904, 2907, \
2910, 2913, 2916, 2931, 2934, 2937, 2940, 2943, 2946, 2958, 2961, \
2964, 2967, 2970, 2973, 2976, 2985, 3012, 3015, 3018, 3021, 3024, \
3027, 3042, 3045, 3048, 3051, 3054, 3057, 3069, 3072, 3075, 3078, \
3081, 3084, 3087, 3096, 3102, 3105, 3108, 3120, 3126, 3129, 3147, \
3150, 3156, 3159, 3162, 3165, 3168, 3174, 3180, 3186, 3189, 3192, \
3195, 3198, 3201, 3204, 3207, 3210, 3216, 3219, 3240, 3246, 3249, \
3258, 3261, 3264, 3267, 3270, 3276, 3279, 3285, 3291, 3294, 3297, \
3402, 3405, 3408, 3417, 3420, 3426, 3429, 3450, 3456, 3459, 3462, \
3465, 3468, 3471, 3480, 3486, 3489, 3492, 3495, 3498, 3501, 3504, \
3507, 3510, 3516, 3519, 3528, 3540, 3546, 3549, 3561, 3564, 3567, \
3570, 3576, 3579, 3582, 3591, 3594, 3597, 3609, 3612, 3615, 3618, \
3621, 3624, 3627, 3642, 3645, 3648, 3651, 3654, 3657, 3672, 3675, \
3678, 3681, 3684, 3687, 3690, 3702, 3705, 3708, 3714, 3720, 3726, \
3729, 3741, 3750, 3756, 3759, 3762, 3765, 3768, 3780, 3786, 3789, \
3792, 3795, 3798, 3801, 3804, 3807, 3810, 3816, 3819, 3825, 3840, \
3846, 3849, 3852, 3861, 3864, 3867, 3870, 3876, 3879, 3891, 3894, \
3897, 3906, 3912, 3915, 3918, 3921, 3924, 3927, 3942, 3945, 3948, \
3951, 3954, 3957, 3960, 3972, 3975, 3978, 3981, 3984, 3987, 4017, \
4023, 4026, 4029, 4032, 4035, 4038, 4053, 4056, 4059, 4062, 4065, \
4068, 4071, 4083, 4086, 4089, 4092, 4095, 4098, 4107, 4125, 4128, \
4137, 4152, 4158, 4167, 4170, 4173, 4176, 4179, 4182, 4185, 4197, \
4203, 4206, 4209, 4215, 4218, 4230, 4236, 4239, 4251, 4257, 4260, \
4263, 4269, 4275, 4278, 4281, 4287, 4290, 4293, 4296, 4302, 4305, \
4308, 4317, 4320, 4326, 4329, 4350, 4356, 4359, 4362, 4365, 4368, \
4371, 4380, 4386, 4389, 4392, 4395, 4398, 4503, 4506, 4509, 4512, \
4518, 4521, 4527, 4530, 4536, 4539, 4560, 4563, 4569, 4572, 4578, \
4581, 4587, 4590, 4593, 4596, 4602, 4605, 4608, 4617, 4620, 4623, \
4629, 4632, 4635, 4638, 4650, 4653, 4659, 4671, 4680, 4683, 4689, \
4692, 4695, 4698, 4701, 4710, 4713, 4716, 4719, 4725, 4728, 4731, \
4752, 4758, 4761, 4782, 4785, 4791, 4803, 4806, 4809, 4812, 4815, \
4821, 4827, 4830, 4836, 4839, 4851, 4857, 4860, 4863, 4869, 4872, \
4875, 4890, 4893, 4896, 4902, 4905, 4908, 4917, 4920, 4923, 4926, \
4932, 4935, 4938, 4950, 4953, 4956, 4962, 4965, 4968, 4971, 4980, \
4983, 4986, 5013, 5016, 5019, 5028, 5031, 5034, 5037, 5043, 5046, \
5049, 5061, 5064, 5067, 5073, 5076, 5079, 5082, 5091, 5094, 5097, \
5103, 5106, 5109, 5124, 5127, 5130, 5136, 5139, 5142, 5148, 5160, \
5163, 5169, 5172, 5178, 5184, 5187, 5190, 5193, 5196, 5208, 5214, \
5217, 5238, 5241, 5247, 5268, 5271, 5274, 5280, 5283, 5286, 5289, \
5298, 5301, 5304, 5307, 5310, 5316, 5319, 5328, 5340, 5346, 5349, \
5361, 5364, 5367, 5370, 5376, 5379, 5382, 5391, 5394, 5397, 5403, \
5406, 5409, 5412, 5418, 5421, 5427, 5430, 5436, 5439, 5460, 5463, \
5469, 5472, 5478, 5481, 5487, 5490, 5493, 5496, 5601, 5604, 5607, \
5610, 5613, 5619, 5628, 5631, 5634, 5637, 5640, 5643, 5649, 5670, \
5673, 5679, 5682, 5691, 5694, 5697, 5703, 5706, 5709, 5712, 5718, \
5721, 5724, 5730, 5736, 5739, 5742, 5748, 5760, 5763, 5769, 5781, \
5784, 5790, 5793, 5796, 5802, 5814, 5817, 5820, 5823, 5826, 5829, \
5832, 5841, 5847, 5862, 5871, 5874, 5892, 5901, 5904, 5907, 5910, \
5913, 5916, 5928, 5931, 5934, 5937, 5940, 5943, 5946, 5961, 5964, \
5967, 5970, 5973, 5976, 5982, 6012, 6015, 6018, 6021, 6024, 6027, \
6039, 6042, 6045, 6048, 6051, 6054, 6057, 6072, 6075, 6078, 6081, \
6084, 6087, 6093, 6102, 6105, 6108, 6120, 6123, 6129, 6132, 6135, \
6138, 6147, 6150, 6153, 6159, 6174, 6180, 6183, 6189, 6192, 6195, \
6198, 6201, 6204, 6207, 6210, 6213, 6219, 6231, 6234, 6237, 6240, \
6243, 6249, 6258, 6270, 6273, 6279, 6285, 6291, 6294, 6297, 6309, \
6312, 6315, 6318, 6321, 6324, 6327, 6342, 6345, 6348, 6351, 6354, \
6357, 6372, 6375, 6378, 6381, 6384, 6387, 6390, 6402, 6405, 6408, \
6417, 6420, 6423, 6429, 6432, 6435, 6438, 6450, 6453, 6459, 6471, \
6480, 6483, 6489, 6492, 6495, 6498, 6501, 6504, 6507, 6510, 6513, \
6519, 6528, 6531, 6534, 6537, 6540, 6543, 6549, 6570, 6573, 6579, \
6582, 6591, 6594, 6597, 6702, 6705, 6708, 6714, 6720, 6723, 6729, \
6732, 6735, 6738, 6741, 6750, 6753, 6759, 6780, 6783, 6789, 6792, \
6795, 6798, 6801, 6804, 6807, 6810, 6813, 6819, 6825, 6831, 6834, \
6837, 6840, 6843, 6849, 6852, 6870, 6873, 6879, 6891, 6894, 6897, \
6903, 6912, 6915, 6918, 6921, 6924, 6927, 6930, 6942, 6945, 6948, \
6951, 6954, 6957, 6972, 6975, 6978, 6981, 6984, 6987, 7014, 7023, \
7026, 7029, 7032, 7035, 7038, 7041, 7053, 7056, 7059, 7062, 7065, \
7068, 7083, 7086, 7089, 7092, 7095, 7098, 7104, 7125, 7128, 7134, \
7140, 7143, 7146, 7149, 7152, 7158, 7164, 7182, 7185, 7194, 7203, \
7206, 7209, 7215, 7218, 7230, 7236, 7239, 7245, 7248, 7251, 7254, \
7260, 7263, 7269, 7281, 7284, 7290, 7293, 7296, 7302, 7305, 7308, \
7314, 7320, 7326, 7329, 7341, 7350, 7356, 7359, 7362, 7365, 7368, \
7380, 7386, 7389, 7392, 7395, 7398, 7401, 7410, 7413, 7416, 7419, \
7425, 7428, 7431, 7452, 7458, 7461, 7482, 7485, 7491, 7503, 7506, \
7509, 7512, 7518, 7521, 7524, 7530, 7536, 7539, 7542, 7548, 7560, \
7563, 7569, 7581, 7584, 7590, 7593, 7596, 7602, 7605, 7608, 7614, \
7620, 7623, 7629, 7632, 7635, 7638, 7641, 7650, 7653, 7659, 7680, \
7683, 7689, 7692, 7695, 7698, 7803, 7806, 7809, 7812, 7815, 7821, \
7824, 7830, 7836, 7839, 7842, 7845, 7851, 7854, 7860, 7863, 7869, \
7890, 7893, 7896, 7902, 7905, 7908, 7914, 7920, 7923, 7926, 7932, \
7935, 7938, 7941, 7950, 7953, 7956, 7962, 7965, 7968, 7980, 7983, \
7986, 8013, 8016, 8019, 8025, 8031, 8034, 8037, 8043, 8046, 8049, \
8052, 8061, 8064, 8067, 8073, 8076, 8079, 8091, 8094, 8097, 8103, \
8106, 8109, 8124, 8127, 8130, 8136, 8139, 8142, 8145, 8154, 8157, \
8160, 8163, 8169, 8172, 8175, 8190, 8193, 8196, 8205, 8214, 8217, \
8235, 8241, 8247, 8250, 8253, 8256, 8259, 8265, 8271, 8274, 8295, \
8301, 8304, 8307, 8310, 8316, 8319, 8325, 8340, 8346, 8349, 8352, \
8361, 8364, 8367, 8370, 8376, 8379, 8391, 8394, 8397, 8403, 8406, \
8409, 8412, 8415, 8421, 8427, 8430, 8436, 8439, 8451, 8457, 8460, \
8463, 8469, 8472, 8475, 8490, 8493, 8496, 8502, 8514, 8517, 8520, \
8523, 8526, 8529, 8532, 8541, 8547, 8562, 8571, 8574, 8592, 8601, \
8604, 8607, 8610, 8613, 8619, 8625, 8631, 8634, 8637, 8640, 8643, \
8649, 8652, 8670, 8673, 8679, 8691, 8694, 8697, 8703, 8706, 8709, \
8712, 8715, 8721, 8724, 8730, 8736, 8739, 8742, 8745, 8751, 8754, \
8760, 8763, 8769, 8790, 8793, 8796, 8901, 8904, 8907, 8910, 8913, \
8916, 8925, 8931, 8934, 8937, 8940, 8943, 8946, 8952, 8961, 8964, \
8967, 8970, 8973, 8976, 9012, 9015, 9018, 9021, 9024, 9027, 9036, \
9042, 9045, 9048, 9051, 9054, 9057, 9063, 9072, 9075, 9078, 9081, \
9084, 9087, 9102, 9105, 9108, 9120, 9123, 9126, 9132, 9135, 9138, \
9147, 9150, 9153, 9156, 9162, 9165, 9168, 9174, 9180, 9183, 9186, \
9201, 9204, 9207, 9210, 9213, 9216, 9231, 9234, 9237, 9240, 9243, \
9246, 9258, 9261, 9264, 9267, 9270, 9273, 9276, 9285, 9306, 9312, \
9315, 9318, 9321, 9324, 9327, 9342, 9345, 9348, 9351, 9354, 9357, \
9360, 9372, 9375, 9378, 9381, 9384, 9387, 9402, 9405, 9408, 9417, \
9420, 9423, 9426, 9432, 9435, 9438, 9450, 9453, 9456, 9462, 9465, \
9468, 9471, 9480, 9483, 9486, 9501, 9504, 9507, 9510, 9513, 9516, \
9528, 9531, 9534, 9537, 9540, 9543, 9546, 9561, 9564, 9567, 9570, \
9573, 9576, 9582, 9603, 9612, 9615, 9618, 9621, 9624, 9627, 9630, \
9642, 9645, 9648, 9651, 9654, 9657, 9672, 9675, 9678, 9681, 9684, \
9687, 9702, 9705, 9708, 9714, 9720, 9723, 9726, 9732, 9735, 9738, \
9741, 9750, 9753, 9756, 9762, 9765, 9768, 9780, 9783, 9786, 9801, \
9804, 9807, 9810, 9813, 9816, 9825, 9831, 9834, 9837, 9840, 9843, \
9846, 9852, 9861, 9864, 9867, 9870, 9873, 9876}

There are 1548 by actual count.

Math Is Fun Forum

#1 2011-12-02 01:48:41

probability

#2 2011-12-02 02:29:07

Re: probability

#3 2011-12-02 02:36:03

Re: probability

#4 2011-12-02 07:03:41

Re: probability

#5 2011-12-02 07:46:28

Re: probability

#6 2011-12-04 02:40:48

Re: probability

#7 2011-12-04 05:05:15

Re: probability

#8 2011-12-05 05:02:25

Re: probability

#9 2011-12-05 06:52:57

Re: probability

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