Answer to Question #140823 in Discrete Mathematics for Mahesh Daulat Rayate

Question

A box contains 6 white balls and 6 black balls. Find number of ways 4 balls can be
drawn from the box if
i) Two must be white
ii) All of them must have same color

Answer 1

i) if we choose 2 white balls, then we choose 2 black balls too.

The number of ways of choosing 2 white(also for black) balls from 6 is: $C^{2}_6$

Then, the number of ways of choosing 2 white and 2 black balls is:

$C^{2}_6*C^{2}_6=\frac{6!}{2!*4!}*\frac{6!}{2!*4!}=225$

ii) All chosen balls can be either black or white.

The number of ways of choosing 4 white(also for black) balls from 6 is: $C^{4}_6$

Then, the number of ways of choosing 4 white or 4 black balls is:

$C^{4}_6+C^{4}_6=2*C^{4}_6=2*\frac{6!}{2!*4!}=30$