Out of 6 boys and 4 girls, a group of 7 is to be formed. In how many ways can this be done if group

English

Gujarati

Hindi

6.Permutation and Combination

medium

Out of $6$ boys and $4$ girls, a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys

A

$120$

B

$90$

C

$100$

D

$80$

Solution

(c) $1$ girl and $6$ boys ${ = ^4}{C_1}{ \times ^6}{C_6} = 4$

$2$ girls and $5$ boys ${ = ^4}{C_2}{ \times ^6}{C_5} = 36$

$3$ girls and $4$ boys ${ = ^4}{C_3}{ \times ^6}{C_4} = 60$

Hence total ways $60 + 36 + 4 = 100$.

Standard 11

Mathematics

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