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

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(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?

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