This is a classic permutation problem.
We are given the number of permutations of 10 things taken 3 at a
time. Note: ORDER MATTERS because President, Vice-President,
and Treasurer are ordered by rank.
The needed formula is
P(n, r) = n!/(n - r)!
P(10, 3) = 10!/(10 - 3)!
P(10, 3) = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(7 x 6 x 5 x 4 x 3 x 2 x 1)
We cancel out 7 factorial down to 1 factorial on the top and bottom.
This leaves us with 10 x 8 x 9.
P(10, 3) = 10 x 9 x 8
P(10, 3) = 90 x 8
P(10, 3) = 720
Answer: 720 committees are possible.
Did you follow? This is a probability question regarding permutation.