Data Management: Premutations Problem With identical Items

[gurjant]

Homework Statement

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

Homework Equations

n! factorials

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

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

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.