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How many different 3-digit numbers can be formed, such that tens digit
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08 Aug 2023, 03:29
08 Aug 2023, 03:29
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How many different 3-digit numbers can be formed, such that tens digit is prime?
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Re: How many different 3-digit numbers can be formed, such that tens digit
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09 Aug 2023, 05:11
09 Aug 2023, 05:11
2
This is a permutation question. Best to use the slot method here.
Slot 1: the hundreds digit
Here we only have the restriction that it cannot be 0, since it would then be a two digit number. So, there are 9 possible choices.
Slot 2: the tens digit
Here we have the restriction that the digit must be prime. Therefore, only 2,3,5 and 7 are possible. This gives us 4 choices.
Slot 3: the ones digit
No restrictions. All 10 are okay.
Total: 9*4*10=360.
Slot 1: the hundreds digit
Here we only have the restriction that it cannot be 0, since it would then be a two digit number. So, there are 9 possible choices.
Slot 2: the tens digit
Here we have the restriction that the digit must be prime. Therefore, only 2,3,5 and 7 are possible. This gives us 4 choices.
Slot 3: the ones digit
No restrictions. All 10 are okay.
Total: 9*4*10=360.
How many different 3-digit numbers can be formed, such that tens digit
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19 Jan 2024, 00:02
19 Jan 2024, 00:02
1
Single's digit = 0 to 9 - we can put one of 10 digits there.
Ten's digit = 2,3,5,7, - we can put one of 4 digits there. Since only prime numbers are allowed.
Hundred's digit = 1-9 we can put one of 9 digits there. Since we need a 3-digit number, zero is not allowed.
So in total we have \(10 \times 4 \times 9 = 360\) different 3-digit numbers that satisfy the criteria.
Ten's digit = 2,3,5,7, - we can put one of 4 digits there. Since only prime numbers are allowed.
Hundred's digit = 1-9 we can put one of 9 digits there. Since we need a 3-digit number, zero is not allowed.
So in total we have \(10 \times 4 \times 9 = 360\) different 3-digit numbers that satisfy the criteria.
