Mathematics 9709 · AS & A Level · Permutations and combinations

Permutations and combinations — practice question

Pick 2 letters at random from the 10 letters in the word ZOOLOGICAL.

(a)[4]

Find the number of different arrangements of the 10 letters in the word ZOOLOGICAL where the three Os stay together and the two Ls are not adjacent.

(b)[3]

Find the number of different arrangements of the 10 letters in the word ZOOLOGICAL in which there are exactly 5 letters between the two Ls.

(c)[3]

Find the probability that these two letters are not the same.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use of $\frac{8!}{2!}$ is shown” …