The Indian Cricket team consists of 16 players. It includes 2 wicketkeepers and 5 bowlers. In how many ways can you select a cricket team of eleven players if you have to select 1 wicketkeeper and at least 4 bowlers?Choices:- 1024 1028 1092 1084

To solve this problem, we need to use the concept of combinations in probability.

Step 1: Select 1 wicketkeeper out of 2. This can be done in 2C1 ways.

Step 2: Select 4 bowlers out of 5. This can be done in 5C4 ways.

Step 3: Now, we have selected 5 players (1 wicketkeeper and 4 bowlers). We need to select 6 more players to make a team of 11. The remaining players are 9 (16 total - 2 wicketkeepers - 5 bowlers). This can be done in 9C6 ways.

So, the total number of ways to select the team is 2C1 * 5C4 * 9C6.

Calculating these values:

2C1 = 2 5C4 = 5 9C6 = 84

So, the total number of ways = 2 * 5 * 84 = 840

But, we also have the option to select 5 bowlers. This can be done in 5C5 ways which is 1. The remaining players to be selected are 5 which can be done in 9C5 ways which is 126.

So, the total number of ways to select the team with 5 bowlers is 2C1 * 5C5 * 9C5 = 2 * 1 * 126 = 252

Adding both scenarios, the total number of ways to select the team is 840 + 252 = 1092.

So, the correct answer is 1092.