In a group of 6 boys and 4 girls,four childre | vedclass

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

Question

(D) Total number of children $= 6 + 4 = 10$.We need to select $4$ children out of $10$.The total number of ways to select $4$ children from $10$ is gi

Vedclass · Accepted Answer

$209$

Vedclass · Answer

(D) Total number of children $= 6 + 4 = 10$.We need to select $4$ children out of $10$.The total number of ways to select $4$ children from $10$ is given by ${}^{10}C_4 = \frac{10 	imes 9 	imes 8 	imes 7}{4 	imes 3 	imes 2 	imes 1} = 210$.The condition is that at least one boy must be selected.This is equivalent to: (Total ways) - (Ways with no boys).Ways with no boys means selecting $4$ girls from the $4$ available girls,which is ${}^{4}C_4 = 1$.Therefore,the number of ways to select at least one boy $= 210 - 1 = 209$.

In a group of $6$ boys and $4$ girls,four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

Similar Questions

The number of ways to distribute $25$ apples among $4$ boys,such that each boy receives at least $4$ apples,is:

There are $15$ buses running between Delhi and Mumbai. In how many ways can a man go to Mumbai and return by a different bus?

In how many ways can $10$ people line up at a ticket window of a cinema hall?

The number of points,having both coordinates as integers,that lie in the interior of the triangle with vertices $(0,0)$,$(0,41)$,and $(41,0)$ is:

$\sum\limits_{r = 0}^m {^{n + r}{C_n} = } $

Vedclass Test Series

Exam Paper Generator

Online Exam Module