PERMUTATIONS
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Formula:
[tex] : \: \implies \sf \large P(n, r) = \Large \frac{n!}{(n-r)!} [/tex]
#1
[tex]\implies \sf \large P(10, 5) = \Large \frac{10!}{(10-5)!} [/tex]
[tex]\implies \sf \large P(10, 5) = \Large \frac{10!}{5!} [/tex]
[tex]\implies \sf \large P(10, 5) = 10 \times 9 \times 8 \times 7 \times 6[/tex]
[tex]\implies \sf \large \purple{ P(10, 5) = 30240} \\ \\ [/tex]
#2
[tex]\implies \sf \large \purple{0! = 1} \\ \\ [/tex]
#3
[tex]\implies \sf \large P(11, 11) = \Large \frac{11!}{(11-11)!} [/tex]
[tex]\implies \sf \large P(11, 11) = \Large \frac{11!}{0!} [/tex]
[tex]\implies \sf \large P(11, 11) = \Large \frac{11!}{1} [/tex]
[tex]\implies \sf \large P(11, 11) = 11![/tex]
[tex]\implies \sf \large \purple{ P(11, 11) =39916800}[/tex]
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