Mathematics 9709 · AS & A Level · Permutations and combinations
Permutations and combinations — practice question
Alissa owns $10$ books from the Squares and Circles series. Apart from their colours, the books all appear alike. The set contains $3$ blue books, $2$ red books, $2$ yellow books, $1$ orange book, $1$ purple book and $1$ green book. She lines the books up on a shelf, and she cares only about the colour sequence.
(a)[1]
How many distinct colour orderings can be formed from the $10$ books?
(b)[2]
How many distinct colour orderings of the $10$ books have the $3$ blue books together, but the $2$ yellow books not adjacent?
(c)[3]
How many distinct colour orderings are there of the $10$ books with exactly $4$ books between the $2$ yellow books?
(d)[4]
Find the number of different selections if the $4$ books contain at least $1$ red book, at most $1$ blue book and exactly $1$ yellow book.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate calculation $\frac{10!}{2!3!2!}=151200$.” …