Question

A box contains 6 black and 7 red balls determine how many ways 2 black and 3 red ball

Answer 1

please clarify your question properly.

Answer 2

Given:

A box contains 6 black and 7 red balls

To Find:

how many ways 2 black and 3 red ball can be drawn from the lot.

Solution:

We can see that the total number of  balls = 13

Number of black balls = 6 and

Number of red balls = 7

We need to draw  2black balls and 3 red balls.

Number of ways of choosing r objects from a lot of n objects is given by,

• $nC_r$

Therefore the number of ways in which we can choose 2 black balls and 3 red balls,

• 6$C_2$ x 7$C_3$ = 6! / (2! 4!) x 7! / ( 4! 3!)
• = 5x6/2  x 5x6x7 / 2x3
• = 15 x 35 = 525

The number of ways in which we can choose 2 black balls and 3 red balls is 525.