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?
Accepted Solution
A:
Answer: 1,306,951,360Step-by-step explanation:Number of digits in Number system = 10Number of letters in English Alphabet= 26Number 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:-[tex]10\times26^5[/tex] (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:-[tex]10^2\times26^5[/tex] (2)Now, total product codes are possible: [Adding (1) and (2)] [tex]10\times26^5+10^2\times26^5[/tex] [tex]=26^5(10+10^2)\\\\=(11881376)(10+100)\\\\=11881376(110)\\\\=1306951360[/tex]Hence, the number of product codes are possible = 1,306,951,360