The number of ways, in which 16 oranges can be distributed to four children such that each…

Question

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

Accepted Answer

To distribute 16 oranges to 4 children such that each child gets atleast one orange.

First distribute one orange to each child so that each child get atleast one.

Now, distribute remaining ( $n=12$ ) oranges to ( $r=4$ ) children using beggar's method $={}^{n+r-1}{C}_{r-1}$

$\begin{gathered} ={}^{12+4-1}{C}_{4-1}={}^{15}{C}_{3} \ =\frac{15	imes 14	imes 13}{3	imes 2	imes 1}=5	imes 7	imes 13=455 \end{gathered}$

Solutions · 1