# Variations with repetition

I am having a problem with solving this. How many 7 digit numbers can be formed with digits 1,2,3,4,5,6,7,8 if the digit 2 appears in each number at least twice. I thought of using variations with repetitions but i am not sure how to use it properly since i have the minimum number of repetition of a selected digit.

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• How many 7-digit numbers (with no 9 or 0 digits) are there with precisely two 2s?
• How many 7-digit numbers (with no 9 or 0 digits) are there with precisely three 2s?
• How many 7-digit numbers (with no 9 or 0 digits) are there with precisely four 2s?
• ......
• How many 7-digit numbers (with no 9 or 0 digits) are there with precisely seven 2s?
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oh I'm stupid ..Thanks xD –  Irrational Apr 11 '12 at 19:35
$\ \ \ A=$the number of 7-digit numbers with no twos
$\ \ \ B=$the number of 7-digit numbers with exactly one two.