Q. How many 4 digits even numbers have all 4 digits distinct?

July 2, 2011

The total number of 4 digit even numbers with all distinct digits can be calculated as follows

Count of numbers ending with ‘0’ is 9 x 8 x 7 = 504.

Count of numbers ending with 2 is 9 x 8 x 7 = 504 – Count of numbers starting with ‘0’
= 504 – 8 x 7 = 504 – 56 = 448.
Similarly count of numbers ending with 4, 6 and 8 are 448.

Adding all the counts for even numbers we get 2296.

There are 2296 four digit even numbers that have all 4 digits distinct.

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