Answer:
Step-by-step explanation:
Lets understand how to solve the permutations.
Let the example is [tex]^{5}P_{2}[/tex].
[tex]^{5}P_{2}=\frac{5!}{(5-2)!}[/tex]
[tex]=\frac{5!}{3!}[/tex]
= [tex]\frac{5\times 4\times 3\times 2\times 1}{3\times 2\times 1}[/tex]
= [tex]\frac{5\times 4\times 3!}{3!}[/tex] [Since 3×2×1 = 3!]
= 20
Now we will solve the question given,
Number of ways Dave can put 7 cars together = [tex]^{23}P_{7}[/tex]
[tex]^{23}P_{7}=\frac{23!}{(23-7)!}[/tex]
[tex]=\frac{23!}{16!}[/tex]
[tex]=\frac{23\times 22\times 21\times 20\times 19\times 18\times 17\times 16!}{16!}[/tex]
[tex]=23\times 22\times 21\times 20\times 19\times 18\times 17[/tex]
[tex]=1235591280[/tex]
