Question

A city distributes vehicle identification stickers using a combination of letters followed by a combination of​ digits, each of which may be used more than once. determine the number of possible stickers under the given circumstances. ​a) using 44 letters and 22 ​digits, how many stickers are​ possible? ​b) using 22 letters and 44 ​digits, how many stickers are​ possible? ​c) adding 1 letterletter before the 44 letters and 22 ​digits, how many stickers are​ possible?

Answer 1

A) 672750
B) 68250
C) 2960100

Explanation
A)  We have 26 letters from which to choose 4, and 10 digits from which to choose 2:
$_{26}C_4\times_{10}C_2=\frac{26!}{4!22!}\times\frac{10!}{2!8!}=14950\times45=672750$

B) We have 26 letters from which to choose 2, and 10 digits from which to choose 4:
$_{26}C_2\times_{10}C_4=\frac{26!}{2!24!}\times\frac{10!}{4!6!}=325\times210=68250$

C) We have 26 letters from which to choose 5, and 10 digits from which to choose 2:
$_{26}C_5\times_{10}C_2=\frac{26!}{5!21!}\times\frac{10!}{2!8!}=65780\times45=2960100$