a phone company wants to create some new area codes. Each new area code will have 3 numbers. Using the digits 1, 5, and 7 only once in each code, how many new codes can the phone company create?
157
175
571
517
715
751
Can you think of any others?
To find out how many new codes the phone company can create, we need to calculate the number of permutations of the digits 1, 5, and 7 taken 3 at a time.
The formula to calculate permutations is nPr = n! / (n - r)!, where n is the total number of items and r is the number of items being selected.
In this case, we have 3 digits (1, 5, and 7) and we want to select 3 at a time. So the formula becomes:
3P3 = 3! / (3 - 3)! = 3! / 0! = 3! = 3 * 2 * 1 = 6
Therefore, the phone company can create 6 new area codes using the digits 1, 5, and 7 only once in each code.