### Brain Teasers

# Less than 3 Million

How many 7 digit EVEN numbers less than 3,000,000 can be formed using the digits, 1, 2, 2, 3, 5, 5, and 6?

### Hint

You must account for the identical digits to make sure you don't double count.### Answer

If the digit:1 is first and 2 is last, there are 60 ways to form a 7 digit even number less than 3,000,000.

1 is first and 6 is last, there are 30 ways to form a 7 digit even number less than 3,000,000.

2 is first and 6 is last, there are 60 ways to form a 7 digit even number less than 3,000,000.

2 is first and 2 is last, there are 60 ways to form a 7 digit even number less than 3,000,000.

So, adding up all the different combinations that can be formed we get:

60+30+60+60 = 210.

In total, 210 ways to form a 7 digit even number less than 3,000,000 using the digits 1, 2, 2, 3, 5, 5, and 6.

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