Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
A committee of $6$ people, with at least $4$ men and at least $1$ woman, is to be selected from $10$ men and $9$ women.
(i)[3]
Determine the number of different committees that may be formed.
(ii)[2]
Find the probability that a chosen man, Albert, and a chosen woman, Tracey, are both on the committee.
(iii)[3]
Find the number of possible committees that contain Albert or Tracey, but not both.
(iv)[3]
The committee selected has $4$ men and $2$ women. They line up at random for refreshments. Find the probability that the women are not adjacent in the queue.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Using suitable combinations such as $^ {10}C_4\times ^9C_2$ or $^ {10}C_5\times ^9C_1$” …