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#1 2007-09-01 19:38:06
- teo
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- Registered: 2007-08-04
- Posts: 7
permutation and combination
five married couples are to be seated in a row of ten adjacent seats for a concert. in how many ways can they be seated if
(I) each couple must sit together
(II) all the men sit in a group while all the women sit together given that no husband sits next to his wife.
the answer is (I) 3840 and (II) 23040
to take the first step is easy, to climb up the mountain is another matter.
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#2 2007-09-01 22:23:23
- mathsyperson
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- Registered: 2005-06-22
- Posts: 4,900
Re: permutation and combination
(I)
As each couple has to be stuck together, you only have five things to move around. That means that the amount of arrangements is 5! = 120.
However, there is also a choice as to whether the man or woman sits on the left for each couple.
This choice is present 5 times, and so the total amount of arrangements is 2^5 * 5! = 32*120 = 3840.
(II)
This time, the men and women sit separately. From the same reasoning as before, the 5 men can be arranged in 5! = 120 ways.
The women are a bit more complicated, because the man sitting on the end cannot have his wife sat next to him. That means that there are only 4 choices for the position next to him. The remaining 4 womens' seats can be filled any way, so the women can be arranged in 4 * 4! = 96 ways.
Combining these amounts, there are 120*96 = 11520 ways of arranging the people. There is also another choice to make, because the group of men could be sat on the left or on the right. The answer must be double to account for this and so the final total is 11520*2 = 23040 arrangements.
Why did the vector cross the road?
It wanted to be normal.
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#3 2007-09-03 01:56:18
- teo
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- Registered: 2007-08-04
- Posts: 7
Re: permutation and combination
thank you 
to take the first step is easy, to climb up the mountain is another matter.
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#4 2007-09-03 20:03:07
- landof+
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- Registered: 2007-03-24
- Posts: 131
Re: permutation and combination
Ah, yes. Permutation and Combination. An interesting subject. Don't mean to be annoying... Theres a P & C calculator here, right?
I shall be on leave until I say so...
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#5 2017-02-19 14:59:32
- Monox D. I-Fly
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- From: Indonesia
- Registered: 2015-12-02
- Posts: 2,000
Re: permutation and combination
Ah, yes. Permutation and Combination. An interesting subject. Don't mean to be annoying... Theres a P & C calculator here, right?
Sometimes the matter is he doesn't know whether to use P or C. It's not that simple. Calculators can't help us if we don't even know which ones to use.
Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.
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