Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

At a dog show, there are $10$ spaniels, $14$ retrievers and $6$ poodles. $7$ dogs are chosen to progress to the final.
(a(i))[4]

In how many ways can $7$ distinct dogs be chosen if the selection must contain at least $1$ spaniel, at least $2$ retrievers and at least $3$ poodles?

(a(ii))[3]

$2$ spaniels, $2$ retrievers and $3$ poodles reach the final. They are lined up. How many distinct arrangements of these $7$ dogs are possible if the spaniels stay together and the retrievers stay together?

(a(iii))[3]

How many different arrangements of these $7$ dogs are there if no poodle stands next to another poodle?

Worked solution & mark scheme

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