Official solution
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