A group of diplomats is to be chosen to represent three islands, $K$, $L$ and $M$. The group i

Question

A group of diplomats is to be chosen to represent three islands, $K$, $L$ and $M$. The group is to consist of $8$ diplomats and is chosen from a set of $12$ diplomats consisting of $3$ from $K$, $4$ from $L$ and $5$ from $M$. Find the number of ways in which the group can be chosen if it includes $2$ diplomats from $K$, $3$ from $L$ and $3$ from $M$,[2] diplomats from $L$ and $M$ only,[2] at least $4$ diplomats from $M$,[2] at least $1$ diplomat from each island.[4]

Accepted Answer

(i) $120$ (ii) $9$ (iii) $210$ (iv) $485$

N2008 P2 Q10

N2008 P2 Q10

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