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Re: How many numbers between 0 and 1670 [#permalink]
I tried another way, but can't see what I am missing.
The number of ways the thousand's digit can be filled is 2 - 0 and 1
For each of these ways the hundreds digit can be filled in 7 ways - 0,1,2,3,4,5,6
For each of these ways, the tens digit can be filled in 4 ways - 2,3,5,7
For each of these ways, the units digit can be filled in 4 ways - 2,3,5,7
This gives us 2x7x4x4=224 ways
But since the numbers can't cross 1670, we can subtract the 4 ways of units' digit for the 7 in tens' digit. This would give me 220 ways. Anyone who can see where I am wrong?
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Re: How many numbers between 0 and 1670 [#permalink]
RavindraShah wrote:
I tried another way, but can't see what I am missing.
The number of ways the thousand's digit can be filled is 2 - 0 and 1
For each of these ways the hundreds digit can be filled in 7 ways - 0,1,2,3,4,5,6
For each of these ways, the tens digit can be filled in 4 ways - 2,3,5,7
For each of these ways, the units digit can be filled in 4 ways - 2,3,5,7
This gives us 2x7x4x4=224 ways
But since the numbers can't cross 1670, we can subtract the 4 ways of units' digit for the 7 in tens' digit. This would give me 220 ways. Anyone who can see where I am wrong?


Using FCP we can do it like this:
_ _ (for 2 digit) = 4*4 = 16
_ _ _ (for 3 digit) = 9*4*4 = 144

But for 4 digits we will have to break it down into the range of 1000-1599 and 1600-1670 because 1577 will be included but 1677 will be not and if we try to limit the 10's digit to 3 (2,3,5) 1577 and such pairs will not be counted.
So, calculate 1000-1599 and then 1600-1670

For 1000-1599: _ _ _ _ (4 digits) = 1*6*4*4 = 96
For 1600-1670: _ _ _ _ (4 digits) = 1*1*3*4 = 12; because 1657, 1627, 1637 will be included but 1677 will not be included.

So total: 16+144+96+12 = 268
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Re: How many numbers between 0 and 1670 [#permalink]
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Re: How many numbers between 0 and 1670 [#permalink]
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