There are 13 players of cricket, out of which 4 are bowlers. In how ma

1.	There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team eleven be selected from them so as to include at least two bowlers? A. 72 B. 78 C. 42 D. none of these.
Answer» Option : (B) 4 out of 13 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 2 bowlers. ∴ Number of ways = ⁴C₂ x ⁹C₉ + ⁴C₃ x ⁹C₈ + ⁴C₄ x ⁹C₇ = 6 + 36 + 36 = 78.

There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team eleven be selected from them so as to include at least two bowlers? A. 72 B. 78 C. 42 D. none of these.

Answer»

Option : (B)

4 out of 13 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 2 bowlers.

∴ Number of ways = ⁴C₂ x ⁹C₉ + ⁴C₃ x ⁹C₈ + ⁴C₄ x ⁹C₇

= 6 + 36 + 36

= 78.