JEE MainMathematicsEasyPermutations and Combinations

Consider a class of 5 girls and 7 boys. The number of different
teams consisting of 2 girls and 3 boys that can be formed from this
class, if there are two specific boys A and B, who refuse to be the
members of the same team, is

Show answer and solution

Without any restriction, total number of ways of forming team
is

\ ^{7}C_{3} \times \ ^{5}C_{2} = 350

. If two specific boys are in
same team then total number of ways of forming team equals to

\ ^{5}C_{1} \times \ ^{5}C_{2} = 50

ways total ways =350 - 50=300 ways

Source: Grass-G / M-28 Mathematics Paper FST 16 Jan.docx

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