Question

1 point
A Box contains 6 white balls
and 4 black balls. In how many
ways can one select 3 white
and 2 black from this box.
O a) 20
O b) 6
O c) 120
O d) 14​

Answer 1

Answer: 3 white and 2 black balls from box of 6 white balls and 4 black balls can be selected in 120 ways. Hence answer is c)120

Step-by-step explanation:

GIVEN: Box contains 6 white balls and 4 black balls

TO SELECT: 3 white and 2 black balls from this box

SOLUTION:

To find 3 white and 2 black balls from box of 6 white balls and 4 black balls, we will use the combination formula (refer to attachment).

Out of 6 white balls, 3 can be selected in,

6C3 ways,

i.e, $\frac{6!}{3! (6-3)!}$ =  $\frac{6!}{3! 3!}$  = $\frac{6*5*4*3!}{3!*3!}$ =  $\frac{6*5*4}{3*2*1}$  = 20 ways

and,

Out of 4 black balls, 2 can be selected in,

4C2ways,

i.e, $\frac{4!}{2! (4-2)!}$ =  $\frac{4!}{2! * 2!}$  = $\frac{4*3*2!}{2!*2!}$ =  $\frac{4*3}{2*1}$  = 6 ways

Hence, 3 white and 2 black balls from box of 6 white balls and 4 black balls can be selected in 20 x 6 = 120 ways.

Answer 2

The correct answer is option (b) 6,

Explanation:

• A Box contains 6 white balls and 4 black balls.
• In 6 ways can one select 3 white and 2 black from this box.