Question

A box contains 5 different red and 6 different white balls. In how many ways can 6 balls be selected so that there are at least two balls of each color?

Answer 1

The selection of 6 balls, consisting of at least two balls of each color from 5 red and 6 white balls can be made in the following ways:

Red balls (5)	White balls(6)	Number of ways
$2$	$4$	${}^5{C}_2{\times }^6{C}_4=150$
$3$	$3$	${}^5{C}_3{\times }^6{C}_3=200$
$4$	$2$	${}^5{C}_4{\times }^6{C}_2=75$
	Total	$425$