A father with 8 children takes them 3 at a ti | vedclass

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(B) Let the total number of children be $n = 8$. The father takes $r = 3$ children at a time.Total number of ways to select $3$ children out of $8$ is

Vedclass · Accepted Answer

$21$

Vedclass · Answer

(B) Let the total number of children be $n = 8$. The father takes $r = 3$ children at a time.Total number of ways to select $3$ children out of $8$ is given by the combination formula ${^n}{C_r} = {^8}{C_3} = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$.Each trip involves $3$ children. Therefore,the total number of 'child-trips' is $56 	imes 3 = 168$.Since there are $8$ children and each child is treated equally,the number of times each child goes to the garden is $\frac{168}{8} = 21$.Alternatively,for a specific child to be included in a group of $3$,the father must choose $2$ more children from the remaining $7$ children. This can be done in ${^7}{C_2} = \frac{7 	imes 6}{2 	imes 1} = 21$ ways.

$A$ 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

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