Question

Determine the number of ways to choose a set of 9 pencils from a selection of 10.

Answer 1

label the pencils:
a b c d e f g h i j
choosing 9 of them will exclude one. There are 10 pencils, so 10 opportunities to exclude one of them. So there are 10 ways, to answer your question.

Answer 2

The number of ways to choose a set of 9 pencils from a selection of 10 is 10.

Explanation:

According to the combination formula, the total number of ways to select r items from total n items is

`^nC_r=(n!)/(r!(n-r)!)`

Total number of pencils = n = 10

Number of selected pencils = r = 9

The number of ways to choose a set of 9 pencils from a selection of 10 is

`^(10)C_(9)=(10!)/(9!(10-9)!)`

`^(10)C_(9)=(10* 9!)/(9!1!)`

`^(10)C_(9)=10`

Therefore the number of ways to choose a set of 9 pencils from a selection of 10 is 10.