Q1.(9pts)Given 5 pairs of gloves (all 10 gloves can be considered distinct, sinc
ID: 3184693 • Letter: Q
Question
Q1.(9pts)Given 5 pairs of gloves (all 10 gloves can be considered distinct, since even a matching pair have a right and a left glove.), in how many ways can 5 different people choose two gloves with no one getting a matching pair? Hint: Let NA.) i=1, 2, 3, 4, 5 be the number of ways in which 5 people each choose two gloves with the ith person getting a matching pair. Use Formula # of ways to distribute r different objects into 5 different boxes with ri objects in box) is (r1)(r2) (r3)!(4)(rs)! Show a r! ying what is A,, each S, and N. Write answer in terms of C(n,r) and /or factorials.Explanation / Answer
The answer is 5280 if everyone must have a left and a right glove. That's 5! !5. See http://en.wikipedia.org/wiki/Derangementfor the calculation of !5, the derangements of 5 things = the permutations of 5 things where none are in their original spot. BTW, !n has a simple formula: integer part of (n! / e)
One might assume that everyone chooses a left glove and a right glove, but as stated, there's no reason make the assumption, IMHO.
If a person can have 2 gloves for the same hand, the answer is 65280.
EDIT: I found the full article here: http://www.maa.org/sites/default/files/p...
It is based on inclusion-exclusion principles.
I find it tough reading, even with some background in the subject. Derangements are much more complicated than combinations and permutations.
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