Question 958245: How many numbers greater than 100 can be formed using the digits 1,2,3,4,5 if no digit may be repeated?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 1 digit numbers: can't do because we need the number to be bigger than 100
2 digit numbers: can't do because we need the number to be bigger than 100
3 digit number: so numbers like 123 or 345. We have 5 choices and 3 slots, so P(5,3) = (5!)/(5-3)! = (5!)/(2!) = 120/2 = 60. There are 60 different 3 digit numbers
4 digit numbers: P(5,4) = (5!)/(5-4)! = (5!)/(1!) = 120/1 = 120. There are 120 different 4 digit numbers
5 digit numbers: P(5,5) = (5!)/(5-5)! = (5!)/(0!) = 120/1 = 120. There are 120 different 5 digit numbers
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Add up the results: 60+120+120 = 300
There are 300 different numbers that can be formed that are greater than 100. These numbers either have 3 digits, 4 digits or 5 digits.
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