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

Answer 1

i) 2 red,4 black => C(5,2)*C(6,4) =150
ii)3 red,3 black => C(5,3)*C(6,3) =200
iii)4red,2 black => C(5,4)*C(6,2) =75

Therefore total number of ways =
150+200+75 = 425 ways
Hope this helps! Cheers! :)