Question 514939: How many different numbers can be formed from the digits 0, 1, 3, 5, 7, 9 such that each number is between 2000 and 4000 ?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
If the numbers can be repeated:
We can choose the first digit only 1 way, (it must be 3).
We can choose the 2nd digit as either 0, 1, 3, 5, 7, 9. That's 1*6 ways.
For each of those 6 ways we can choose the first two digits, we can
choose the 3rd digit as either 0, 1, 3, 5, 7, 9. That's 1*6*6 ways.
For each of those 1*6*6 ways we can choose the first three digits, we can
choose the 4th digit as either 0, 1, 3, 5, 7, 9. That's 1*6*6*6 ways.
Answer 1*6*6*6 = 6³ = 216
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If the numbers cannot be repeated:
We can choose the first digit only 1 way, (it must be 3).
We can choose the 2nd digit as either 0, 1, 5, 7, 9. That's 1*5 ways.
For each of those 5 ways we can choose the first two digits, we can
choose the 3rd digit any of 4 ways. That's 1*5*4 ways.
For each of those 1*5*4 ways we can choose the first three digits, we can
choose the 4th digit any of 3 ways. That's 1*5*4*3 ways.
Answer 1*5*4*3 = 60.
Edwin
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