Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

(i)[1]

Find how many different arrangements can be formed from the $9$ letters of TOADSTOOL if the three Os stay together and the two Ts stay together.

(ii)[4]

Find how many different arrangements of the $9$ letters in TOADSTOOL have the two Ts separated.

(iii)[2]

Find the probability that a random arrangement of the $9$ letters in TOADSTOOL has a T in the first position and a T in the last position.

(iv)[4]

Choose five letters from the $9$ letters of TOADSTOOL. Find how many different selections are possible if the five letters contain at least $2$ Os and at least $1$ T.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correctly evaluates $6!=720$

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