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Probability Level 3

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


The answer is 78.

Vraj Mistry by Vraj Mistry , 21, India

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1 solution

There are 3 possible scenarios: 2, 3 or 4 bowlers.

In the first scenario, 2 bowlers (out of 4) are required, and all 9 non-bowlers will play the game.

4 ! 2 ! × 2 ! = 6 \frac{4!}{2! \times 2!} = 6

In the second scenario, 3 bowlers (out of 4) are required, and 8 (out of 9) non-bowlers will play the game.

4 ! 3 ! × 1 ! × 9 ! 8 ! × 1 ! = 36 \frac{4!}{3! \times 1!} \times \frac{9!}{8! \times 1!} = 36

In the last scenario, all 4 bowlers will play the game, and 7 (out of 9) non-bowlers will play the game.

9 ! 7 ! × 2 ! = 36 \frac{9!}{7! \times 2!} = 36

As a result, there are 6 + 36 + 36 = 78 6 + 36 + 36 = 78 possibilities.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You actually didn't need to take three cases . Since there are 9 batsmen and 4 bowlers in the team of 11 there have to be atleast 2 bowlers if all the 9 batsmen are included. So u could just simply do 13C11 which gives us 78 as the correct ans.

Aditya Kumar - 5 years ago

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