Question

There are 6 bowlers and 9 batsmen in a cricket club. In how many ways can a team of 11 be selected so that the team contains at least 4 bowlers?

A) 1170 B) 1200 C) 720 D) 360

Answer 1

Answer:

1170

Step-by-step explanation:

In the above problem, the given condition is "at least 4 bowlers".

So the no. of bowlers has to be ≥4

• BOWLERS(6)       BATSMEN (9)     TOTAL(11)      COMBINATION

               4                        7                           11                ⁶C₄×⁹C₇

               5                        6                           11                ⁶C₅×⁹C₆

               6                        5                           11                ⁶C₆×⁹C₅

Now add the combination ⇒ ⁶C₄×⁹C₇+⁶C₅×⁹C₆+ ⁶C₆×⁹C₅⇒ 1170