Out of a classroom of 6 boys and 4 girls

Out of a classroom of 6 boys and 4 girls the teacher picks a president for the student board, a vice president and a secretary. What is the probability that only girls will be elected?

(A) 8/125.
(B) 2/5.
(C) 1/30.
(D)1/720.
(E) 13/48.

The best answer is C.
The basic principle of this question is that one person can’t be elected to more than one part, therefore when picking a person for a job the “inventory” of remaining people is growing smaller.
The probability of picking a girl for the first job is 4/10 = 2/5.
The probability of picking a girl for the second job is (4-1)/(10-1) = 3/9.
The probability of picking a girl for the third job is (3-1)/(9-1) = 1/4.
The probability of all three events happening is: 2/5 x 3/9 x ¼ = 1/30.