Question

A product code consists of a one-or two-digit number (including 0) followed by 5 not necessarily distinct letters. How many product codes are possiable?

Answer 1

1188137600

Explanation:

this is a 2 part problem

first, you have the one-digit number and 5, not distinct letters

and then you have 2-digit numbers and 5, not distinct letters

for the first part you will have the 10 possible numbers (combination 10, choose 1) and 26^5 letter combos multiply those two together and get 118813760

part two is similar, 2 diget numbers between 10 and 99 is 90 possible numbers (basic math) and 26^5 possible letter combos which is 1069323840

add those two togeter to get 11881376000

Answer 2

Answer: 1,306,951,360

Explanation:

Number of digits in Number system = 10

Number of letters in English Alphabet= 26

Number of ways to product code consists of a one digit number (including 0) followed by 5 not necessarily distinct (repetition is allowed) letters will be:-

`10*26^5` (1)

Number of ways to product code consists of a two-digit number (including 0) followed by 5 not necessarily distinct (repetition is allowed) letters will be:-

`10^2*26^5` (2)

Now, total product codes are possible: [Adding (1) and (2)]
`10*26^5+10^2*26^5`

`=26^5(10+10^2)\\\\=(11881376)(10+100)\\\\=11881376(110)\\\\=1306951360`

Hence, the number of product codes are possible = 1,306,951,360