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

Answer:

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

Step-by-step explanation:

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

$^nC_r=\frac{n!}{r!(n-r)!}$

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

$^{10}C_{9}=\frac{10!}{9!(10-9)!}$

$^{10}C_{9}=\frac{10\times 9!}{9!1!}$

$^{10}C_{9}=10$

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