Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

Put one peg into each of the four holes shown. The pegs are in different colours, and any pegs with the same colour are identical.
(i)[1]

Calculate the number of different arrangements of coloured pegs in the four holes, using 6 pegs, each of a different colour.

(ii)[1]

Calculate the number of different arrangements of coloured pegs in the four holes, using 4 pegs made up of 2 blue pegs, 1 orange peg and 1 yellow peg.

(iii)[1]

Calculate how many different arrangements of coloured pegs in the 4 holes Beryl can make using 4 distinct colours.

(iv)[3]

Calculate how many different arrangements of coloured pegs in the 4 holes Beryl can make using 3 distinct colours.

(v)[3]

Calculate how many different arrangements of coloured pegs in the 4 holes Beryl can make using any of her 12 pegs.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correctly evaluate $^6P_4 = \frac{6!}{2!}=360$

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