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625. Here's how:

There are five odd digits {1,3,5,7,9} so our numbers will be made using only these digits. This is the same number of possibilities as if you had a base 5 number system where the allowed digits are {0,1,2,3,4}. For a 1 digit base-5, there are 5 possibilities, for a two digit base-5 there are 5² = 25 possibilities, so for a 4-digit, there are 5^4 = 625possible. This is the same number you will have with only using odd digits.

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Q: How many 4 digit numbers have only odd numbers?
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