Permutations combinatorics problem?

In summary, there are a total of 4,536 different telephone extensions with four digits and no repeated digits, where the first digit cannot be zero. This is calculated using the formula P(n,r)=n!/(n-r)! with 9 possibilities for the first digit and P(9,3)=9!/6!=9x8x7 for the last three digits. The final result is 9x9x8x7=4,536.
  • #1
SMA_01
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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?
 
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  • #2
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?

Seems fine to me.
 

FAQ: Permutations combinatorics problem?

1) What is a permutation in combinatorics?

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.

2) What is the formula for calculating permutations?

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.

3) Can you give an example of a permutation problem?

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.

4) How is a permutation different from a combination?

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.

5) How can I use permutations in real life?

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.

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