The number of ways five complete outfits could be arranged if Johnny had 20 complete living room outfits is 1,860,480 ways
Permutation has to do with arrangement.
Since Johnny had 20 complete living room outfits, for him to arrange different sets of five complete outfits, he can do it in 20P5 number of ways.
The permutation formula is as shown below:
[tex]^n P_r =\frac{n!}{(n-r)!}[/tex]
Hence:
[tex]^{20}P_5=\frac{20!}{(20-5)!}\\ ^{20}P_5=\frac{20!}{(15)!}\\^{20}P_5=\frac{20\times19\times 18 \times 17 \times 16 \times 15!}{15!}\\^{20}P_5=20\times19\times 18 \times 17 \times 16 \\^{20}P_5=1,860,480ways[/tex]
Hence the number of ways five complete outfits could be arranged if Johnny had 20 complete living room outfits is 1,860,480 ways.
Learn more on permutation here: https://brainly.com/question/23779115
