Question

I was trying to get help earlier but my internet went out

Answer 1

We have two expressions of permutations and combinations. We have to expand and simplify the expression:

`(_8P_5)/(_8C_5)=(P(8,5))/(C(8,5))`

We can expand the permutation as:

`\begin{gathered} P(n,r)=(n!)/((n-r)!) \\ P(8,5)=(8!)/((8-5)!)=(8!)/(3!) \end{gathered}`

and the combination as:

`\begin{gathered} C(n,r)=(n!)/(r!(n-r)!) \\ C(8,5)=(8!)/(5!(8-3)!)=(8!)/(5!3!) \end{gathered}`

Then, combining the two as:

`(P(8,5))/(C(8,5))=((8!)/(3!))/((8!)/(5!3!))=(1)/(5!)=(1)/(120)`

Answer: the quotient is equal to 1/120.