How many ways of giving six oranges to four persons ?
Suppose that there may be those who cannot get one.
Suppose that there may be those who cannot get one.
Answer
84 ways
Solution
It is better for you to consider the way of placing which places both six oranges and three sticks.
The number of the ways of placing six oranges and three sticks on nine places is the same as the number of the ways of choosing which chooses three from nine.
It is 84 ways (9 × 8 × 7) / (3 × 2 × 1) = 84.
<Another solution> There is a way of dividing as follows:
(1) 6 = 6+0+0+0 4 ways,
(2) 6 =5+1+0+0 12 ways,
(3) 6=4+2+0+0 12 ways,
(4) 6=4+1+1+0 12 ways,
(5) 6=3+3+0+0 6 ways,
(6) 6=3+2+1+0 24 ways,
(7) 6=3+1+1+1 4 ways,
(8) 6=2+2+2+0 4 ways,
(9)6=2+2+1+1 6 ways
There are 84 ways in total.
