Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

Hannah selects $5$ singers from $15$ applicants to take part in a concert. She arranges the $5$ singers in the sequence they will perform. Out of the $15$ applicants, $10$ are female and $5$ are male.
(i)[2]

How many different lists can Hannah form?

(ii)[2]

Determine the number of lists for which the first performer is male, the second is female, the third is male, the fourth is female and the fifth is male.

(iii)[3]

Find the number of distinct selections of $5$ performers with more males than females.

(iv)[3]

Two of the applicants are Mr and Mrs Blake. Find the number of different selections that include Mr and Mrs Blake and also satisfy Ami’s requirement.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply $^{15}P_5$ or an implied $^{15}C_5$

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