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

Sagot :

Cdbuckidn
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:

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

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

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

[tex]^{10}C_{9}=\frac{10!}{9!(10-9)!}[/tex]

[tex]^{10}C_{9}=\frac{10\times 9!}{9!1!}[/tex]

[tex]^{10}C_{9}=10[/tex]

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

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