(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?