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Question

A father with 8 children takes 3 at a time to the Zoological gardens, as often as he can without taking the same 3 children together more than once.

The number of times he will go to the garden is?


A

56

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B

21

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C

112

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D

None of these

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Solution

The correct option is A

56


The explanation for the correct option :

Step 1: Given conditions:

Number of children 'n'=8

Number of children taken at a time 'r'=3

Condition: Father visits the garden without taking the same 3 children together more than once

Step 2: Calculate the number of possibilities:

Number of times he goes to the garden=Crn

Substitute the value of 'n'and 'r'in the formula Crn=n!(n-r)!r!

We get C38=8!(8-3)!3!

=8!5!3!=56

Hence, Option(A) is the correct answer.


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