All even?

How many five digit numbers (10000 to 99999) have all even digits?


The answer is 2500.

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2 solutions

Ossama Ismail
Feb 6, 2017

The first digit has only 4 values (2,4,6,8)

All other digits have 5 values (0,2,4,6,8)

Numbers that have even digits = 4 × 5 4 = 2500 4 \times 5^4 = 2500

Geoff Pilling
Feb 6, 2017

There are 4 possibilities for the first number and 5 for the others.

4 5 4 = 2500 4 \cdot 5^4 = \boxed{2500}

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