Question

There are 5 good hitters and 4 poor hitters on the bench in baseball game Choose 3 player
random in how many ways can we choose at least 2 good hitters​

Answer 1

In 50 ways, we can choose at least 2 good hitters.

Step-by-step explanation:

There are 5 good hitters and 4 poor hitters on the bench in baseball game.

We have to choose 3 players in which at least 2 good hitters.

We can choose 2 good hitters, 1 poor hitter and 3 good hitters.

Number of ways of choosing 2 good hitters and 1 poor hitter  = $5_{C_{2} } \times 4_{C_{1} }$                                                                                         = $\frac{5\times 4\times 3!}{2!\times 3!} \times \frac{4\times 3!}{3!}$

= $10\times 4$

= 40 ways

Number of ways of choosing 3 good hitters = $5_{C_{3} } = \frac{5\times 4\times 3!}{2!\times 3!}$ = 10 ways

Number of ways we can choose 2 good hitters = 40 + 10 = 50 ways

Hence, in 50 ways we can choose at least 2 good hitters.