how many 5-digit numbers can be created using the digits 2,3,4,5, and 6 without repeating any digits in that five-digit number?
To determine the number of 5-digit numbers that can be created using the digits 2, 3, 4, 5, and 6 without repeating any digits, you can use the concept of permutation. The formula for calculating permutations is:
nPr = n! / (n - r)!
where n is the total number of objects and r is the number of objects taken at a time.
In this case, n = 5 (since there are 5 digits: 2, 3, 4, 5, and 6) and r = 5 (since we need to form 5-digit numbers). Plugging these values into the permutation formula:
5P5 = 5! / (5 - 5)!
Calculating 5! (5 factorial):
5! = 5 x 4 x 3 x 2 x 1 = 120
Substituting the value of 5! back into the permutation formula:
5P5 = 120 / (5 - 5)!
The denominator becomes 0! which is equal to 1:
5P5 = 120 / 1
Therefore, the number of 5-digit numbers that can be created using the digits 2, 3, 4, 5, and 6 without repeating any digits is equal to 120.