The number of ways in which 10 balls can be selected from 10 identical green balls, 10 identical blue balls and 9 identical red balls are

Step-by-step solution

Required number of ways = coefficient of x 10 in x 0 + x 1 + x 2 + . . . . + x 10 2 x 0 + x 1 + x 2 + . . . . + x 9 = coeff. of x 10 in 1 - x 11 1 - x 2 1 - x 10 1 - x = coeff. of x 10 in 1 – x – 3 1 – x 11 2 1 – x 10 = coeff. of x 10 in 1 – x – 3 1 + x 22 – 2 x 11 1 – x 10 = coeff. of x 10 in 1 – x – 3 1 + x 22 – 2 x 11 – x 10 – x 32 + 2 x 21 = coeff. of x 10 in 1 – x – 3 1 – x 10 – 2 x 11 + 2 x 21 + x 22 – x 32 = coeff. of x 10 in 1 – x – 3 – coeff. of x 0 in 1 – x – 3 = 10 + 3 - 1 C 10 - 1 = 12 C 10 - 1 = 12 × 1