How many different numbers can you create out of the five digits: 1,2,3,4,5 ?
There are 5 choices for the first digit, 4 choices for the second, 3 choices for the third, ...
The choices are independent of each other, so we multiply the number of choices to get the count of different numbers:
5*4*3*2*1 = ?
The above answer assumes all 5 digits are used, and without repetition.
another interpretation.
single digit number = 5
double digit number = 5x4 = 20
triple ditit number = 5x4x3 = 60
four digit numbers = 5x4x3x2 = 120
five digit numbers = 5x4x3x2x1 = 120
add them up
To determine the number of different numbers that can be created out of the five digits 1, 2, 3, 4, and 5, we need to calculate the number of permutations. A permutation is an arrangement of elements where the order matters and repetitions are not allowed.
To solve this problem, we can use the formula for the number of permutations of choosing k elements from a set of n elements, which is given by:
P(n, k) = n! / (n - k)!
Here, n is the total number of elements in the set (5 in this case) and k is the number of elements being chosen to create a number (k can range from 1 to n).
In this case, since we are creating numbers using all 5 digits, k = n = 5. Thus, the formula becomes:
P(5, 5) = 5! / (5 - 5)! = 5! / 0! = 5! / 1 = 5 x 4 x 3 x 2 x 1 / 1 = 120
Therefore, using the digits 1, 2, 3, 4, and 5, we can create 120 different numbers.