Question 876339: Given the digits 0,1,1,2,4,5,7,7
How many three digit numbers can be made from them?
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
There are 4 types of 3 digit numbers that can be made witrh them.
They are:
ABC, AAB, ABA, ABB
An example of type ABC would be 704.
An example of type AAB would be 115.
An example of type ABA would be 717.
An example of type ABB would be 477.
Case 1: ABC
Choose the digit for A any of 5 ways {1,2,4,5,7} (CAN'T choose 0).
Choose the digit for B any of the remaining 5 ways (CAN choose 0)
Choose the digit for C any of the remaining 4 ways.
Total for case 1: 5*5*4 = 100 ways.
Case 2: AAB
Choose the digit for A any of 2 ways {1,7}
Choose the digit for B any of the remaining 5 ways.
Total for case 2: 2*5 = 10 ways.
Case 3: ABA
Same as Case 2:
Total for Case 3: 10 ways.
Case 4: ABB
Choose the digit for B any of 2 ways {1,7}
Choose the digit for A any of the remaining 4 ways. (CAN'T choose 0)
Total for Case 4: 2*4 = 8.
Grand total: 100+10+10+8 = 128
Edwin
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