A club has 12 members, 5 of whom are senior citizens and the remaining 7 are juniors
MATHEMATICS · Subjective · A Level · Mathematics · Probability · Probability
Problem
A club has 12 members, 5 of whom are senior citizens and the remaining 7 are juniors. A management board of 6 members is to be chosen subject to the condition that the board contains at most two senior citizens.
(a) Calculate the total number of admissible boards by direct enumeration of the admissible senior–junior compositions.
(b) Obtain the same count by first finding the total number of six-member boards and then subtracting the number of boards that contain three or more senior citizens.
(c) If one management board is selected at random from all possible six-member boards, find the probability that the chosen board meets the ‘at most two seniors’ condition.