Question

A father with $8$ children takes $3$ at a time to the zoological garden, 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. $112$
• B. $56$
• C. $336$
• D. None of these

Answer 1

The correct option is B

$56$

Find the number of times of visiting garden by father:

Total number of children are $=8$

Number of ways taking children at a time without taking same $3$ children again $=3$

$\therefore$Required number of visiting $={}^{8}C_3$

$=\frac{8!}{5!\times 3!}$ $\left[\mathbf{\because }{}^{\mathbf{n}}\mathit{C}_{\mathbf{r}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{n}\mathbf{!}}{\left(n-r\right)\mathbf{!}\mathbf{}\mathbf{.}\mathbf{}\mathbf{r}\mathbf{!}}\right]$

$=\frac{8\times 7\times 6}{3\times 2}$

$=\mathbf{56}$

Thus, $\mathbf{56}$ he will visit garden.

Hence, Option ‘B’ is Correct.