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put this solution on YOUR website!Let's look at the first digit:
Since the number goes from 10,500 to 11,000, there is only one possibility for the first number: the only number it can be is "1"
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Let's look at the second digit:
Since the number goes from 10,500 to 11,000, there are two possibilities for the second number. The two possibilities are: 0 and 1
However since 1 is already taken, our only possibility for the second digit is 0
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Let's look at the third digit:
Since the number goes from 10,500 to 11,000, we can have the numbers 5,6,7,8,9 (not zero since it's taken) for the third digit
So we have 5 possibilities for the third digit
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Let's look at the fourth digit:
Now lets use any remaining digits to form the fourth possible digit. The remaining digits are:
2,3,4,5,6,7,8,9
Now lets say our third number is 5, so our possible numbers for the fourth digit is
2,3,4,6,7,8,9 (notice I've excluded 5)
So we'll have 7 possibilities
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Let's look at the fifth digit:
Now lets use any remaining digits to form the fifth possible digit. The remaining digits are:
2,3,4,6,7,8,9
Now lets say our fourth number is 6, so our possible numbers for the fifth digit is
2,3,4,7,8,9 (notice I've excluded 6)
So we'll have 6 possibilities
Now multiply all of these combinations to get:
1*1*5*7*6=210
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You can also look at it like this:
Since we're using a permutation, we can use nPr. So we have 7 possible numbers and we're choosing 3 digits. So we'll get
Start with the given nPr formula
Plug in n=7 and r=3
Subtract
Expand
Cancel like terms
Simplify
Now multiply 7*6*5 to get 210
Notice how this is identical to the previous explanation (the numbers are just in different order)
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