Question 698558: giving digits 2,2,3,3,3,4,4,4,4 how many distinct 4 digits greater than 3000 can be formed?
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
In order to be greater than 3000, the first digit must either be 3 or 4
Case 1. When the first digit is 3:
Then the rest of the digits must come from this list: 2, 2, 3, 3, 4, 4, 4, 4
Therefore we may choose any 3-digit sequence containing only 2's, 3's, & 4's
except we can't choose 222 or 333. So there are 3*3*3 - 2 = 25 for case 1.
Case 2. When the first digit is 4:
Then the rest of the digits must come from this list: 2, 2, 3, 3, 3, 4, 4, 4
Therefore we may choose any 3-digit sequence containing only 2's, 3's, & 4's
except we can't choose 222. So there are 3*3*3 - 1 = 26 for case 2.
Answer = 25+26 = 51
Edwin
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