360 possibilities or ways
1) Gathering the data:
A) We have a 4 person subcommittee to be selected from a 6 people committee
The only restriction to fulfill those vacancies is that there can't be repetition.
Since we have 6 people to 4 vacancies, and the order does not matter. Then We can write this Permutation
6 x 5 x 4 x 3 = 360 possibilities
How many ways can a 4-person subcommittee be selected from a committee of 6 people?
B) Similarly, since this problem does not make any reference if the order of the president's chair or place matters, as well as the other offices:
We have another Permutation of 6 people in 4 places:
P = 6 x 5 x 4 x 3 = 360 possibilities or ways of choosing 1 president, 1 vp, 1 secret. and 1 treasurer
President
Vice President
Secretary
Treasurer