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How many even numbers less than 500 can be formed using the digits 1,2,3,4,5? Each digits may be used only once in any number.

 Feb 17, 2020
 #1
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(2, 4, 12, 14, 24, 32, 34, 42, 52, 54, 124, 132, 134, 142, 152, 154, 214, 234, 254, 312, 314, 324, 342, 352, 354, 412, 432, 452) = 28 such numbers

 Feb 17, 2020
 #2
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Well we know the digit must end in 2 or 4, because it has to be even. So 1, 3, 5, can't be the ending digit.

 

We've chosen 2 digits already (2 and 4), so there are 3 possibilities for the first digit. It can't be 5, because then it would exceed the count of 500, so 1, 3, or whatever's left of 2 and 4. And only 3 digits left for the middle digit. So that means 2 * 3 * 3 = 18 cases for 3 digit numbers..

 

Now what about 2 digit numbers? Having chosen 2 or 4, we have 4 other possibilities left. So 2 * 4 = 8 cases for 2-digit numbers.

 

We have to remember 1 digit numbers, 2 or 4, so 2 cases.

 

In the end: 18 + 8 + 2 = 28 numbers.

 Feb 17, 2020

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