SMA_01 said:Homework Statement
A telephone extension has four digits, how many different extensions are there with no repeated digits, if the first digit cannot be zero?
Homework Equations
P(n,r)=n!/(n-r)!
The Attempt at a Solution
For the first digit, there are 9 possibilities (because no zero)
For the last 3 digits I used P(9,3)=9!/6!=9x8x7
So, in the end my result was: 9x9x8x7= 4,536 different extensions...
I'm just wondering if I was correct?
A permutation is an arrangement of objects or elements in a specific order. In combinatorics, we use permutations to calculate the number of possible ways to arrange a set of objects.
The formula for calculating permutations is n!/(n-r)!, where n represents the total number of objects and r represents the number of objects being arranged.
Sure, let's say we have a set of 5 letters (A, B, C, D, E) and we want to know how many different 3-letter combinations can be made. The answer would be 5!/(5-3)! = 60 possible permutations.
A permutation takes into account the order of objects, while a combination does not. For example, ABC and ACB would be considered different permutations, but the same combination.
Permutations can be used to solve a variety of problems, such as calculating the number of different ways to arrange a set of numbers or letters, determining the number of possible outcomes in a game, or finding the number of possible combinations for a lock code.