Among 14 players, 5 are bowlers. In how many ways a team of 11 may be

1.	Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers? A. 265 B. 263 C. 264 D. 275
Answer» Option : (C) 5 out of 14 players are bowlers. In other words, 9 players are not bowlers. A team of 11 is to be selected so as to include at least 4 bowlers. Number of ways = ⁵C₄ x ⁹C₇ + ⁵C₅ x ⁹C₆ = 180 + 84 = 264

Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers? A. 265 B. 263 C. 264 D. 275

Answer»

Option : (C)

5 out of 14 players are bowlers.

In other words,

9 players are not bowlers.

A team of 11 is to be selected so as to include at least 4 bowlers.

Number of ways = ⁵C₄ x ⁹C₇ + ⁵C₅ x ⁹C₆

= 180 + 84

= 264