How many different ID cards can be made if there are five digits on a card what if digits can be repeated?

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How many different ID cards can be made if there are 6 digits on a card and no digit can be used more than once?

Algebra ->  Permutations -> SOLUTION: in a company, ID cards have 5 digit numbers. a. can be formed if repetition of the digit is allow? b. how many ID cards can be formed if repetition of the digit is not allowed.      Log On

a) If repetion is allowed, then there are 10 ways to choose each of 5 digirs. Hence, by the multiplication rule, we obtain that the total number of possible different ID cards is: "10 \\cdot 10 \\cdot 10 \\cdot 10 \\cdot 10 = 10^5 = 100 000."

b) If repetion are not allowed, then there are 10 ways to choose the first digit, 9(since we have already chosen one digit as the first) ways to choose the second digit, 8 ways to choose the third digit, 7 ways to choose the fourth digit, and 6 ways to choose the fifth digit. Therefore, by the multiplication rule, the answer is:

"10 \\cdot 9 \\cdot 8 \\cdot 7 \\cdot 6 = 30240."