A father with 8 children takes them 3 at a time to Zoological gardens, as often as he can without ta

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6.Permutation and Combination

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A father with $8$ children takes them $3$ 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 each child will go to the garden is

A

$56$

B

$21$

C

$112$

D

None of these

Solution

(b) Each child will go as often as he (or she) can be accompanied by two others.

Therefore the required number is ${^7}{C_2} = 21$.

Standard 11

Mathematics

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