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

Answer: 1,306,951,360

Step-by-step 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:-

$10\times26^5$   (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:-

$10^2\times26^5$    (2)

Now, total product codes are possible:         [Adding (1) and (2)] $10\times26^5+10^2\times26^5$

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

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