(C) The number of times the father can visit the garden is equivalent to the number of ways to choose a group of $3$ children out of $8$ available chi

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) The number of times the father can visit the garden is equivalent to the number of ways to choose a group of $3$ children out of $8$ available children.Since the order of children in the group does not matter,we use the combination formula $^nC_r = \frac{n!}{r!(n-r)!}$.Here,$n = 8$ and $r = 3$.Therefore,the required number of ways is $^8C_3 = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56$.Thus,the father will go to the garden $56$ times.

Competitive Quantitative Aptitude Permutation and Combination Permutation and Combination

Easy

$A$ 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 he will go to the garden is

A
$336$
B
$112$
C
$56$
D
None of these

Explore More

Browse All

Question Bank

All Subjects

Competitive Questions

Competitive

Quantitative Aptitude Questions

Chapter

Permutation and Combination

Subtopic

Permutation and Combination

$A$ man has $10$ friends. In how many ways can he invite one or more of them to a party?

Easy

View Solution

In how many ways can the letters of the word '$UNIVERSAL$' be arranged when $E, R, S$ are always together?

Medium

View Solution

How many words can be formed using the letters of the word $INDEPENDENCE$,such that all vowels always come together?

Medium

View Solution

There are $10$ persons named $A, B, \dots, J$. We have the capacity to accommodate only $5$. In how many ways can we arrange them in a line if $A$ must be included and $G$ and $H$ must not be included in the team of $5$?

Difficult

View Solution

The total number of $4$-digit numbers which can be formed using the digits $1, 2, 3, 4$ without repetition such that the digit $n+1$ never immediately follows the digit $n$ (for $n=1, 2, 3$) is:

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ 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 he will go to the garden is

Similar Questions

$A$ man has $10$ friends. In how many ways can he invite one or more of them to a party?

In how many ways can the letters of the word '$UNIVERSAL$' be arranged when $E, R, S$ are always together?

How many words can be formed using the letters of the word $INDEPENDENCE$,such that all vowels always come together?

There are $10$ persons named $A, B, \dots, J$. We have the capacity to accommodate only $5$. In how many ways can we arrange them in a line if $A$ must be included and $G$ and $H$ must not be included in the team of $5$?

The total number of $4$-digit numbers which can be formed using the digits $1, 2, 3, 4$ without repetition such that the digit $n+1$ never immediately follows the digit $n$ (for $n=1, 2, 3$) is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module