Question

For the T-20 World Cup, Indian team of 15 players is to be formed from 20 players. Out of 20 players, 7 are batsmen, 7 are bowlers, 5 all-rounders and 1 wicketkeeper. In how many ways this can be done by taking exactly 5 bowlers, 6 batsmen, 1 wicketkeeper and at most 3 all-rounders.

• A. 1470
• B. 1890
• C. 6280
• D. 10
• E. 1

Answer 1

The correct option is A

1470

To select a team of 15, you have to select almost 3 all rounders.
Therefore the required number of ways
= ${}^7$C${}_5$ $\times$ ${}^7$C${}_6$ $\times$ ${}^1$C${}_1$ $\times$ ${}^5$C${}_3$
=1470.