Question

There are 13 cricket players, out of which 4 are bowlers. In how many ways can team of 11 be selected from them so as to include at least 3 bowlers?

Answer 1

There are 4 bowlers in 13 player team.

So, maximum we can add 4 bowlers.

And we need to include at least 3 bowlers.

If we include 3 bowlers then from the remaining 9 [13 – 4 bowlers] players, we need to include 8.

The number of ways, 8 players can be selected among 9 is = ⁹C₈ = 9 The number of ways,

3 players can be selected among 4 is = ⁴C₃ = 4

So, taking 3 bowlers the team can be represented in (9 X 4) = 36 ways.

If we include 4 bowlers then from the remaining 9 [13 – 4 bowlers] players, we need to include 7.

The number of ways, 7 players can be selected among 9 is = ⁹C₇ = 36

The number of ways, 4 players can be selected among 4 is = ⁴C₄ = 1

So, taking 4 bowlers the team can be represented in (36 X 1) = 36 ways.

Therefore, the total possible ways are = (36 + 36) = 72.