From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can…

Question

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is

Aicharya · Accepted Answer

7 Batsmen & 6 Bowlers
To select 10 players including atleast
4 Batsmen & 4 Bowlers
Captain & vice-captain already selected
$\begin{aligned}
& \text { No. of ways }={ }^6 \mathrm{C}_5 \times{ }^5 \mathrm{C}_3+{ }^6 \mathrm{C}_4 \times{ }^5 \mathrm{C}_4+{ }^6 \mathrm{C}_3 \times{ }^5 \mathrm{C}_5 \\ & =6 \times 10+15 \times 5+20 \times 1 \\ & =60+75+20=155
\end{aligned}$ ,

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include…

Solution