# How many 2-digit even numbers can be formed from the digits 1,2, 3, 4, 5 if the digits can be repeated?

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The unit's place of the 2-digit number can be filled in 2 ways (2 or 4). The ten's place of the 2-digit number can be filled in 5 ways (1,2, 3, 4 or 5) since repetition is allowed. So the number of two-digit even numbers that can be formed with repetition is 2 x 5 = 10. The 10 permutations are: 12, 22, 32, 42, 52, 14, 24, 34, 44, 54.

Now if repetition were not allowed, the ten's place can be filled only 4 ways since one of the even numbers is used in the unit's place. So the number of two-digit even numbers that can be formed without repetition is 2 x 4 = 8. The 8 permutations are: 12,  32, 42, 52, 14, 24, 34, 54. Note: we can't form 22 and 44 in this case.

Krishna Laxman
Mathematics Trainer and Educational consultant

Two digit even number :  A numbers between 10 and 99 (including both) and one's digit should be even.

In our case ,the ten's digits can be filled in 5 ways and the one's digit can be filled in 2 ways

so totally $5\cdot2$ = 10 .

How many two-digit numbers can be formed from the numbers 1,2,3,4 is repetirion is allowed