**(c) 425**

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

(a) Selecting 2 red balls out of 5 red balls and 4 white balls out of 6, i.e.,

Number of ways = ^{5}C_{2} x ^{6}C_{4} = \(\frac{5\times4}{2}\times\frac{6\times5}{2}\)

= 10 × 15 = 150

(b) Selecting 3 red balls out of 5 red balls and 3 white balls out of 6, i.e.,

Number of ways = ^{ 5}C_{3} x ^{6}C_{3} = \(\frac{5\times4}{2}\times\frac{6\times5\times4}{3\times2}\)

= 10 × 20 = 200

(c) Selecting 4 red balls out of 5 red balls and 2 white balls out of 6, i.e.,

Number of ways = ^{ 5}C_{3} x ^{6}C_{2} = \(5\times\frac{6\times5}{2}\) = 5 × 15 = 75

∴ Total number of ways of selecting at least two balls of each colour = 150 + 200 + 75 = **425.**