Question

(1 point) How many ways can you give 9 (identical) apples to your 5 favourite Mathematics lecturers (without any restrictions)?

Answer 1

126

Explanation:

Total number of apples = 9

Number of favourite Mathematics lecturers = 5

To find number of ways in which 9 (identical) apples can be given to your 5 favourite Mathematics lecturers, find
`C(9,5)`

Combination refer to selection of items such that order does not matter.

Use
`C(n,p)=(n!)/(p!(n-p)!)`

Put
`n=9,p=5`

`C(9,5)=(9!)/(5!(9-5)!)\\=(9!)/(5!4!)\\=(9(8)(7)(6)5!)/(5!4!) \\=(9(8)(7)(6))/(4(3)(2)(1))\\=126`