Question

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

Answer 1

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:

`C(n,p)=(n!)/(p!(n-p)!)`

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

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

So there are 3003 ways to choose the 5 vessels.