Question 1157599: how many numbers greater than 150 can be formed from the digit 1,2,3,4,5 if no repetitions allowed
Answer by Edwin McCravy(20081)   (Show Source):
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Case 1. The number has 3 digits and the first digit is 1.
There are only three, 152, 153, and 154
Case 2: The number has 3 digits and the first digit is not 1.
(They will all be greater than 150.)
We can choose the first digit 4 ways, (2,3,4,or 5).
We can choose the second digit 4 ways.
We can choose the third digit 3 ways.
That's 4∙4∙3 = 48
Case 3: The number has 4 digits.
(They will all be greater than 150.)
We can choose the first digit 5 ways.
We can choose the second digit 4 ways.
We can choose the third digit 3 ways.
We can choose the fourth digit 2 ways.
That's 5∙4∙3∙2 = 120
Case 4: The number has 5 digits.
(They will all be greater than 150.)
We can choose the first digit 5 ways.
We can choose the second digit 4 ways.
We can choose the third digit 3 ways.
We can choose the fourth digit 2 ways.
We can choose the fifth digit 1 way.
That's 5∙4∙3∙2∙1 = 120
Total for all 4 cases: 3+48+120+120 = 291
Edwin
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