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How many 3-digit numbers can be formed from the digit 1, 2, 3, 4 ,5,6 and 7assuming that (i) repetition of the digit is allowed? (ii) repetition of the digits is not allowed?

How many 3-digit numbers can be formed from the digit 1, 2, 3, 4 ,5,6 and 7assuming that
(i) repetition of the digit is allowed?
(ii) repetition of the digits is not allowed?

Grade:Upto college level

1 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
We need to find a 3 digit number using the digits 1, 2, 3, 4 ,5,6 and 7.
(1) If repetition is allowed
The first digit can be any of 1, 2, 3, 4 ,5,6 and 7 = 7 possibilities.
The second digit can be any of 1, 2, 3, 4 ,5,6 and 7 = 7 possibilities.
The third digit can be any of 1, 2, 3, 4 ,5,6 and 7 = 7 possibilities.
Hence, the total number of ways are = 7.7.7 = 343.
(2) If repetition is not allowed
The first digit can be any of 1, 2, 3, 4 ,5,6 and 7 = 7 possibilities.
The second digit can be any of 1, 2, 3, 4 ,5,6 and 7 except the chosen digit = 6 possibilities.
The third digit can be any of 1, 2, 3, 4 ,5,6 and 7 except the first and second = 5 possibilities.
Hence, the total number of ways are = 7.6.5 = 210.
Thanks & Regards
Latika Leekha
askIITians Fauclty

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