cole is studying ceramics and he was asked to submit 5 vessels from his collection to exhibit at the fair. he has 15. vessels that he thinks are show worthy. in how many ways can the vessels be chosen

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03-11-2022
Mathematics

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cole is studying ceramics and he was asked to submit 5 vessels from his collection to exhibit at the fair. he has 15. vessels that he thinks are show worthy. in how many ways can the vessels be chosen

Sagot :

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DevineR342251idn DevineR342251idn · Answer 1 · 2022-11-03T14:45:51-04:00

Since he has 15 vessels and needs to choose 5, we can use a combination of 15 choose 5 to calculate the number of possible ways, since the order of the vessels inside the group of 5 is not important.

The formula to calculate a combination of n choose p is:

[tex]C(n,p)=\frac{n!}{p!(n-p)!}[/tex]

Then, for n = 15 and p = 5, we have:

[tex]\begin{gathered} C(15,5)=\frac{15!}{5!(15-5)!}=\frac{15!}{5!10!}=\frac{15\cdot14\cdot13\cdot12\cdot11\cdot10!}{5\cdot4\cdot3\cdot2\cdot10!} \\ =\frac{15\cdot14\cdot13\cdot12\cdot11}{5\cdot4\cdot3\cdot2}=3003 \end{gathered}[/tex]

So there are 3003 ways to choose the 5 vessels.

Sagot :

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