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

Step-by-step explanation
A) We have 26 letters from which to choose 4, and 10 digits from which to choose 2:

`_(26)C_4*_(10)C_2=(26!)/(4!22!)*(10!)/(2!8!)=14950*45=672750`

B) We have 26 letters from which to choose 2, and 10 digits from which to choose 4:

`_(26)C_2*_(10)C_4=(26!)/(2!24!)*(10!)/(4!6!)=325*210=68250`

C) We have 26 letters from which to choose 5, and 10 digits from which to choose 2:

`_(26)C_5*_(10)C_2=(26!)/(5!21!)*(10!)/(2!8!)=65780*45=2960100`