Question

a box contains 5 different red and 6 white balls in how many ways can 6 ball be selected so that there are at least 2 balls of each colour

Answer 1

A box contains 5 different red and 6 white balls 
we have 5 red balls and 6 white balls out of these we select 6 balls having at least two balls of each colour
no of ways to choose 6 balls having two balls of each colour = combination of 2 red balls out of 5 * 4 white balls out of 6 + combination of 3 red balls out of 5 * 3 white balls out of 6 + combination of 4 red balls out of 5 * 2 white balls out of 6 
=5c2*6c4 + 5c3*6c3 + 5c4*6c2
=(5*4/2) * (6*5*4*3/4*3*2) + (5*4*3/3*2) * (6*5*4/3*2) + (5*4*3*2/4*3*2) * (6*5/2) 
= 10*15 + 10*20 + 5*15
=150 + 200 + 75
= 425
Total no of ways to choose 6 balls having two balls of each colour = 425

Answer 2

finding lcm of 5 red balls and 6 white balls we can find the answer.and the answer is 30.