How many ways of giving six oranges to four persons ?
I shall give at least one to everyone.
Answer
10 ways
Solution
Think about the way of partition of 6 oranges being set out by putting 3 pieces of stick between oranges.
The number of place putting 3 sticks is five which is the number of gap of oranges.
The number of ways of partition is the same as choosing three out of five which is
(5 × 4 × 3)/ (3 × 2 × 1) =10 ways.
(5 × 4 × 3)/ (3 × 2 × 1) =10 ways.
<Another solution>
6 = 3 + 1 + 1 + 1 and 6 = 2 + 2 + 1 + 1 are the ways of partition.
There are four ways of the first one and six ways of the second for partition.
Then in total, 4 + 6 = 10 ways.
