SOLUTION: five couples want to have their pictures taken. In how many ways can they arrange themselves in a row if
a. Couples must stay together?
b. They may stand anywhere?
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-> SOLUTION: five couples want to have their pictures taken. In how many ways can they arrange themselves in a row if
a. Couples must stay together?
b. They may stand anywhere?
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Question 1178588: five couples want to have their pictures taken. In how many ways can they arrange themselves in a row if
a. Couples must stay together?
b. They may stand anywhere? Answer by ikleyn(52776) (Show Source):
(a) Considering five couples as five special objects,
we have 5! = 5*4*3*2*1 = 120 permutations of these objects.
Next, we have 2 possible permutations (A,B) --> (B,A) inside each of 5 pairs.
These permutations are independent --- so, there are = 32*120 = 3840 permutations of 5 couples, satisfying the imposed conditions.
(b) If no restrictions are imposed, then there are 10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 possible permutations of 10 persons.
