QUESTION to think about

unique · 2006-10-13 03:12:35

how many different ways can the numbers 1,2,3,4 be arranged if you use each number only once?

i got
1,2,3,4
4,1,2,3
3,4,1,2
2,3,4,1
2,1,4,3
1,4,2,3
3,1,4,2
4,3,2,1

any other ways?
and how many can there be....if we just guessed?

Devantè · 2006-10-13 03:25:04

We can use a factorial to find out the different combinations we can use for a sequence like this.

By using 4!, we see that:

4x3x2x1 = 24.

Therefore there are 24 combinations.

I think that is correct...

Last edited by Devanté (2006-10-13 03:25:33)

unique · 2006-10-13 03:26:55

thanks i guess i was using the very very long way

Last edited by unique (2006-10-13 03:27:06)

pi man · 2006-10-13 03:27:34

The answer is 4! (pronounced 4 factorial) which is 4 * 3 * 2 * 1. So the answer is 24.

To help you understand, think about this. How many ways can you arrange 2 numbers? Two, right? 12 and 21.

Now add in a 3rd number. One way of doing this is to take the 2 ways to arrange 2 numbers and add in the 3rd:

12 - Add a 3 in to get 123, 132, and 312
21 - Add a 3 in to get 213, 231, and 321.

So for every solution for 2 numbers, there's 3 ways to add in a 3rd number. So that's 2 * 3 solution.

To add in a 4th number, take each of the 3 digit numbers and work from there:
123 - Add the 4 in to get the following four possibilities: 1234, 1243, 1423, 4123.

So for each of the ways you could make a 3 digit number, there are 4 possibilities when you add in a 4th digit. There are 6 (3*2*1) ways to make a 3 digit number, multiply that by 4 when you add in a fourth digit and you get 24 (4*3*2*1)

unique · 2006-10-13 03:32:05

thanks
now i completly understand

mathsyperson · 2006-10-13 03:38:28

Also, if you're going to write out all the possibilities, it's very useful to use some kind of method to make sure that you've got all of them. It looks like in your list you were just writing them down as you thought of them, which means that you've missed quite a few. A good way is to write them in ascending order as if they were 4-digit numbers.

1234 2134 3124 4123
1243 2143 3142 4132
1324 2314 3214 4213
1342 2341 3241 4231
1423 2413 3412 4312
1432 2431 3421 4321

unique · 2006-10-13 03:39:47

yeah your way is much easier...
i was just putting them down as they came in my head. i didnt have an order

Math Is Fun Forum

#1 2006-10-13 03:12:35

QUESTION to think about

#2 2006-10-13 03:25:04

Re: QUESTION to think about

#3 2006-10-13 03:26:55

Re: QUESTION to think about

#4 2006-10-13 03:27:34

Re: QUESTION to think about

#5 2006-10-13 03:32:05

Re: QUESTION to think about

#6 2006-10-13 03:38:28

Re: QUESTION to think about

#7 2006-10-13 03:39:47

Re: QUESTION to think about

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