brucewaynel8914 brucewaynel8914

Today at 8:27 AM
Mathematics

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Use the formula for nPr to evaluate the following expression. 5P5

Answer :

JeanaShupp JeanaShupp

Today at 8:32 AM

Answer: 120

Step-by-step explanation:

The permutation of n things taken r at a time is given by expression :-

[tex]^nP_r[/tex]

The formula to evaluate [tex]^nP_r[/tex] is given by :-

[tex]^nP_r=\dfrac{n!}{(n-r)}[/tex]

Then , [tex]^5P_5[/tex] will be :-

[tex]^5P_5=\dfrac{5!}{(5-5)!}[/tex]

Since , [tex]n!=n(n-1)(n-2).......(2)(1)[/tex]

Then , [tex]^5P_5=\dfrac{5\times4\times3\times2\times1}{0!}=120\ \ \ \text{Also,}0!=1[/tex]

Therefore, the value of the expression [tex]^5P_5=120[/tex]

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