The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

Question

Quantrex Academy · Accepted Answer

Correct answer: A. 455

Distributing 16 identical oranges to 4 children with each getting at least 1.
Let

x_i \ge 1

for

i = 1,2,3,4

and

x_1+x_2+x_3+x_4 = 16

.
Substituting

y_i = x_i - 1 \ge 0

:

y_1+y_2+y_3+y_4 = 12

.
By stars and bars, number of ways

= \binom{12+3}{3} = \binom{15}{3} = \frac{15 \times 14 \times 13}{6} = 455

.

The number of ways, in which 16 oranges can be distributed to four...