How Many 3-Digit Numbers Are Divisible by 5?

In summary, there are 136 3-digit numbers that are divisible by 5, constructed from the digits 0,1,2,3,4,5,6,7,8,9 using each digit at most once. This is obtained through the formula 9*8 + 8*8 = 136, where 9*8 represents the possible combinations for numbers ending in 0 and 8*8 represents the possible combinations for numbers ending in 5. However, this calculation may undercount by excluding numbers like 105, 205, etc. which should be included.
  • #1
zipup
3
0
1. 3-digit numbers are constructed from the digits 0,1,2,3,4,5,6,7,8,9 using each digit at most once. How many such number are divisible by 5?



2. Just simply permutation, the answer is 136.



3. 8 x 7 x 2 = 128
 
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  • #2


Firstly, 8*7*2 is not equal to 128.

My calculation is:

Firstly for numbers ending in 0,

9*8 possible ways of choosing 2 digits.

For numbers ending in 5,

8*7, since we want to exclude 0

9*8 + 8*7 = 128.
 
  • #3


Sisplat said:
Firstly, 8*7*2 is not equal to 128.

My calculation is:

Firstly for numbers ending in 0,

9*8 possible ways of choosing 2 digits.

For numbers ending in 5,

8*7, since we want to exclude 0

9*8 + 8*7 = 128.

I think this undercounts by excluding the eight numbers 105, 205, etc. (Eight since 505 is still out.) We just want to exclude 0 from the first digit, not from the second.

The counting then becomes 9*8 + 8*8 = 136, which seems to be desired answer.

PS. Why is this filed under "Advanced Physics" instead of "Precalculus Mathematics"?
 

FAQ: How Many 3-Digit Numbers Are Divisible by 5?

What is a 3-digit number permutation problem?

A 3-digit number permutation problem is a math problem that involves finding all possible unique combinations of three digits to create a number. For example, if the digits are 1, 2, and 3, the possible 3-digit numbers are 123, 132, 213, 231, 312, and 321.

How do you solve a 3-digit number permutation problem?

To solve a 3-digit number permutation problem, you can use the following steps:

  • Identify the three digits that will be used in the number
  • List out all possible combinations of the digits
  • Eliminate any duplicates
  • Count the remaining combinations to find the total number of permutations

What is the formula for calculating the number of permutations in a 3-digit number permutation problem?

The formula for calculating the number of permutations in a 3-digit number permutation problem is n! / (n - r)! , where n is the total number of digits and r is the number of digits in each permutation. In this case, n = 3 and r = 3, so the formula becomes 3! / (3 - 3)! = 3! / 0! = 3 x 2 x 1 = 6.

Can repetitions be used in a 3-digit number permutation problem?

Yes, repetitions can be used in a 3-digit number permutation problem. This means that the same digit can be used more than once in a single permutation. For example, if the digits are 1, 2, and 3, the number 111 would be a valid permutation.

What are some real-world applications of 3-digit number permutation problems?

3-digit number permutation problems have various real-world applications, such as:

  • Creating unique identification numbers for products or items
  • Generating random passwords or PIN codes
  • Creating lottery number combinations
  • Designing unique license plate numbers

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