Mathematics 9709 · AS & A Level · Permutations and combinations

Permutations and combinations — practice question

The eight digits $1, 2, 2, 3, 4, 4, 4, 5$ are placed in one row.
(a)[1]

How many distinct arrangements can be made from these 8 digits?

(b)[4]

Find the number of distinct arrangements of the 8 digits in which there is a 2 at the beginning, a 2 at the end and the three 4s are not all together.

(c)[5]

Find the probability that all three digits are different.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate evaluation of permutations using $\frac{8!}{2!3!}$.

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