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Question

In a group of 6 boys and 4 girls, four children are to be selected. In how many ways can they be selected such that at least one boy should be there


A

109

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B

128

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C

138

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D

209

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Solution

The correct option is D

209


Explanation for the correct answer:

There are 6 boys and 4 girls.

Hence, the total number of children is 10.

The ways of selecting 4 children from a group of 10 is given as C410

C410=10!4!6!=210

Hence, there are 210 ways in total of selecting 4children out of 10

Consider the groups in which there are no boys, implying all 4 children are girls.

The ways of forming a group of 4 children with 4girls is given as C44

C44=4!4!0!=1

Hence, there is only 1way a group of 4 children can be formed such that there are no boys in it.

Rest all groups contain at least 1boy in them

Number of ways at least 1boy is selected =Total number of ways- Number of ways in which no boys are selected

Number of ways at least 1boy is selected =210-1=209

Hence there are 209 ways in which the group will contain at least 1boy.

Hence, option Dis the correct answer.


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