Mathematics 9709 · AS & A Level · Permutations and combinations

Permutations and combinations — practice question

(a)[2]

Find the total number of distinct arrangements of the $11$ letters in the word CATERPILLAR.

(b)[4]

Find the total number of distinct arrangements of the $11$ letters in the word CATERPILLAR with an $R$ at the start and an $R$ at the end, and with the two $A$s not together.

(c)[4]

Find the total number of distinct selections of $6$ letters from the $11$ letters of the word CATERPILLAR that include both Rs and at least one A and at least one L.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct factorial expression is $\frac{11!}{2!2!2!}$” …

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