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Each of the five possibilities listed above can be extended in 5 ways by inserting an odd digit in the next place.
This gives a list of 5 × 5 = 25 possibilities with two of the missing three digits filled in. How many possibilities are there when filling in all three missing digits? Penny
Hi Elmer. The digits you know have nothing to do with the digits you don't know. So you simply need to think of how many three digit numbers can you make with only odd digits. There are 5 odd digits: 1, 3, 5, 7, 9. If you select one for the first digit, there are the same five to choose for the second (so for every choice of the first digit, there are five choices for the second). Likewise, there are 5 choices for the third digit for every possible twodigit prefix. So you simply need to multiply the number of choices for each digit together ! Hope this helps,  


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