Option 3 : 132300

**Given:**

We have to create a team of 11 players from a group of 24 players

Total number of wicket keepers = 2

Total number of bowlers = 7

Total number of all-rounders = 6

Total number of batsmen = 9

**Formula used:**

^{n}C_{r} = {n!/r!(n - r)!}

**Concept used:**

When selecting some or all of a finite set of things we use combinations

**Calculation:**

1 wicket-keeper can be selected from 2 in ^{2}C_{1} ways

4 bowlers can be selected from 7 in ^{7}C_{4} ways

4 batsmen can be selected from 9 in ^{9}C_{4} ways

2 all-rounders can be selected from 6 in ^{6}C_{2} ways

Required number of ways = 2C_{1} × 7C4 × 9C4 × 6C2

⇒ 2 × {(7 × 6 × 5 × 4)/(4 × 3 × 2)} × {(9 × 8 × 7 × 6)/(4 × 3 × 2)} × {(6 × 5)/2}

⇒ 30 × 35 × 18 × 7

⇒ 132300

**∴ The required ways are 132300.**