Question

Answer the following question using arrangements with repetition, permutations, or combinations. Be sure to explain why the particular counting technique applies to the problem. A dog shelter is giving away 15 different dogs, but you have room for only 5 of them. How many different dog families could you have

Answer 1

Given

In a dog shelter there are 15 different dogs and there is space for only 5 of them.

Step-by-step explanation

To determine the number of different dogs you could have.

Combinations should be used because no item may be selected more than once and the order does not matter.

`\begin{gathered} 15_(C_5)=(15!)/(5!10!) \\ (15!)/(5!10!)=(15*14*13*12*11*10!)/(5*4*3*2*1*10!) \end{gathered}`
`\begin{gathered} (15*14*13*12*11)/(5*4*3*2*1)=7*13*3*11 \\ 3003. \end{gathered}`

Answer

Hence the number of different dogs you could have is 3003.