Find the number of ways in which seven different toys can be given to three children, if the youngest is to receive three toys and the others receive two toys each.

the number of ways of allocating presents to the first child is \(\left( \begin{array}{c}7\\3\end{array} \right)\left( {{\rm{or }}\left( \begin{array}{l}7\\2\end{array} \right)} \right)\)     (A1)

multiplying by \(\left( \begin{array}{c}4\\2\end{array} \right)\left( {{\rm{or}}\left( \begin{array}{l}5\\3\end{array} \right){\rm{or}}\left( \begin{array}{l}5\\2\end{array} \right)} \right)\)     (M1)(A1)

Note:     Award M1 for multiplication of combinations.

\(\left( \begin{array}{c}7\\3\end{array} \right)\left( \begin{array}{c}4\\2\end{array} \right) = 210\)     A1

[4 marks]