Question 1081901: find how many no between 5000 and 6000 can be formed from the digits 1,2,3,4,5,6
a) if no digits are repeated
b) if repeated digits are allowed
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Part (a)
The number must be between 5000 and 6000 so the number must start with 5. Any other starting point and we're not between 5000 and 6000.
If we pull out the digit '5', we're left with 5 other choices: 1,2,3,4,6
Imagine that the four digit number is composed of 4 slots A through D. The first slot A is locked in at 5. The other 3 slots (slot B,C,D) can change.
Slot B has 5 choices
Once we make a choice, we have 4 choices left for slot C
Slot D will have 3 choices
Overall, there are 5*4*3 = 60 different permutations when it comes to picking 3 items from a set of 5.
The answer to part (a) is 60
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Part (b)
Repeats are allowed now so we can reuse the digit '5' if we want to. There are still 3 slots to fill since the first slot is locked to be 5 (see explanation above).
The slots that aren't locked up (B through D) each have 6 choices giving 6*6*6 = 6^3 = 216 different three-digit combinations
So there are 216 different numbers we can form that are between 5000 and 6000.
The answer to part (b) is 216
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