Question

The number of ways of distributing 12 identical oranges among 4 children so that every child gets at least one orange and none of the child gets more than 4 is

• A. 31
• B. 52
• C. 35
• D. 42

Answer 1

The correct option is A 31

Possible patterns are

$4431=\frac{4!}{2!}=12$ ways

$4422=\frac{4!}{2!2!}=6$ ways

$4332=\frac{4!}{2!}=12$ ways

$3333=1$ way

Total$-12+6+12=1=31$ ways.