Discussion
A cricket team of 11 players from 16 players is to be selected. If three particular players are always included in the team, then the number of ways of selecting the team is
Answer: A
The number of ways is 1287.
If three particular players must be included, 8 more places are filled from the remaining 13 players.
\[ \begin{aligned} \tbinom{13}{8} &= \tbinom{13}{5} \\ &= \frac{13 \cdot 12 \cdot 11 \cdot 10 \cdot 9}{120} \\ &= 1287 \end{aligned} \]
Choosing 11 from 16 without the condition would give 4368. The other values do not equal any natural count for this selection.
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