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Question

From a group of 7 men and 4 ladies a committee of 6 persons is formed, then the probability that the committed contains 2 ladies is:


A

513

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B

511

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C

411

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D

311

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Solution

The correct option is B

511


Explanation for the correct option:

Step:1 Calculate the different ways 6 persons can be selected as mentioned.

Here, the total number of persons is

=7+4=11

Therefore, different ways the committee of 6 persons can be formed out of 11 people is

=C611=11!6!=11×10×9×8×7×6!6!×5×4×3×2=462

Now, different ways 2 girls can be selected out of 4 girls is

=C24=4!2!=6

Again, different ways 2 girls can be selected out of 4 girls is

=C47=7!4!=7×6×5×4!4!×3×2=35

Step: 2 Calculate the required probability.

Hence, the probability that there will be 2 girls in the committee of 6 is

=35×6462=511

Therefore, Option(B) is the correct answer.


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