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]
