Freddie owns $6$ toy cars and $3$ toy buses, and every one of them is different. He picks $4$ toys to take with him on holiday.
(i)[1]
In how many distinct ways can Freddie choose $4$ toys?
(ii)[2]
How many of these selections include both his favourite car and his favourite bus?
(iii)[3]
Freddie arranges these $9$ toys in a line. Find the number of possible arrangements if the buses are all next to each other.
(iv)[3]
Find the number of possible arrangements if there is a car at each end of the line and no buses are adjacent.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Shows ${^9C_4}=126$” …
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