QJEEM19Ma2446: JEE Main 2019 Mathematics - Class 11 JEEM19Ma2446 Solution: Consider a class of 5 girls and 7 boys. The number of different …

From 5 girls 2 girls can be selected

= ⁵C₂ ways

From 7 boys 3 boys can be selected

= ⁷C₃ way

$\therefore$   Total number of ways we can select 2 girls and 3 boys

= ⁵C₂ $\times$ ⁷C₃ ways

When two boys A and B are chosen in a team then one more boy will be chosen from remaining 5 boys.

So, no of ways 3 boys can be chosen when A and B should must be chosen = ⁵C₁ ways

$\therefore$   Total number of ways a team of 2 girl and 3 boys can be made where boy A and B must be in the team = ⁵C₁ $\times$ ⁵C₂ ways

$\therefore$   Required number of ways
= Total number of ways $-$ when A and B are always included.

= ⁵C₂ $\times$ ⁷C₃ $-$ ⁵C₁ $\times$ ⁵C₂

= 300