Data Management: Premutations Problem With identical Items

gurjant

1. The problem statement, all variables and given/known data
Ten students have been nominated for positions of secretary, treasurer, social convenor, and fundraising chair. In how many ways can these positions be filled if the Norman twins are running and plan to switch positions on occasion for fun since no one can tell them apart?

txt book answer:4032

2. Relevant equations
n! factorials

nPr= n!/(n-r)! premutations

n!/(a!b!c!......) premutations with identical items


3. The attempt at a solution
10P4=5040 totals ways nominations can be picked

i don't know how to find the number of ways twins can be picked/ answer

awkward

I guess we are to treat the twins as indistinguishable. So try breaking the problem up into three cases:
(1) No twin holds a position;
(2) Exactly one twin holds a position;
(3) Both twins hold positions.

I think I should warn you that I don't get the book answer. So I'm going to stick my neck out and say that the book is wrong. Of course, it may be that I have misinterpreted the problem. I do that a lot.