Question

• In how many ways can a chairman, a vice chairman, a secretary, and a treasurer be selected from a committee of ten people?

Is it right that i used the equation 10!/4! ?

I don't know if the answer 151200 is correct. Can someone help me? Thanks!

Answer 1

It would simply be
10 x 9 x 8 x 7 or 5040 ways

This is the same as P(10,4) = 10!/(10-4)!
= 10!/8!
= 5040

Answer 2

Think of how many ways you can choose a chairman (10), vice-chairman (9 remaining people), secretary(8), treasurer (7).
Multiply them together using the product rule, and the product is
10*9*8*7
=10*9*8*7*6*5*4*3*2*1/(6*5*4*3*2*1)
=10!/(10-4)!