The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is _ _ _ _ _

Step-by-step solution

Given, We have to distribute 20 identical oranges to 3 children, Let children A get O A oranges, children B gets O B oranges and children C gets O C oranges, So, O A + O B + O C = 20 Now this can be distributed using the multinomial theorem, So, Number of ways will be, = coefficient of x 20 in x + x 2 + … . + x 18 3 = coefficient of x 20 in x 3 1 + x + x 2 + … . x 17 3 = coefficient of x 17 in 1 - x 18 1 - x 3 = coefficient of x 17 in ( 1 - x ) - 3 = C 2 19 = 171 As we know that expansion of ( 1 - x ) -