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

I was trying to get help earlier but my internet went out-example-1

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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.

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