Question

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

Answer 1

Answer:

126

Step-by-step 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 $C(n,p)=\frac{n!}{p!(n-p)!}$

Put $n=9,p=5$

$C(9,5)=\frac{9!}{5!(9-5)!}\\=\frac{9!}{5!4!}\\=\frac{9(8)(7)(6)5!}{5!4!} \\=\frac{9(8)(7)(6)}{4(3)(2)(1)}\\=126$