UPSC NDA Math Model Paper 8

The ways of selecting a batsman out of 4=‌4C1=4
The ways of selecting 2 batsmen out of 4=‌4C2=6
The ways of selecting a bowler out of 4=‌4C1=4
The ways of selecting 2 bowlers out of 4=‌4C2=6
The ways of selecting an all-rounder out of 2=‌2C1=2
The ways of selecting 2 all-rounders out of 2=‌2C2=1
The ways of selecting a captain out of 1 = 1
The ways of selecting are = (2 batsmen, a bowler, an all-rounder and a captain) or (a batsman, 2 bowlers, an all-rounder and a captain) or (a batsmen, a bowler, 2 all-rounders and a captain)
∴ Ways of selecting the group = (6 × 4 × 2 × 1) + (4 × 6 × 2 × 1) + (4 × 4 × 1 × 1)
Ways of selecting the group = 112