Get Started With Combinatorics 2 – Adding Another Person

Probability Level 1

Since Alice, Bob, and Charlie were having so much fun standing in lines , their friend Donna decided to join the party.

Now there are four people. How many possible orderings are they if they all want to stand in a line?

Image credit: WIkipedia DaniDF 1995


The answer is 24.

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Arron Kau by Arron Kau

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8 solutions

Arron Kau Staff
May 7, 2014

We could list out the number of ways, as in the previous question. However, this will take some time to do so. Instead, we will use the rule of product to approach this question.

There are 4 choices for the person in the first position.
After which, there are 3 choices for the person in the second position.
After which, there are 2 choices for the person in the third position.
After which, there are 1 choices for the person in the last position.


Hence, there are 4 × 3 × 2 × 1 = 24 4 \times 3 \times 2 \times 1 = 24 possible orderings.

15 Helpful 0 Interesting 0 Brilliant 0 Confused

4! permutation and combination

neel jha - 7 years, 1 month ago
Parth Lohomi
Jul 2, 2014

answer is definitely 4!

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Kevin Patel
May 9, 2014

4 ! = 4 3 2*1 =24 order pairs

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Kris Randall
May 5, 2015

I just figured out that with just one person staying in front of the line there were 6 possible ways for the other 3 to be switched around. With that being said, that would leave 3 other people that could be in the front. So I then multiplied 6 by 4 and got my answer.

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Kentucky Potrido
Jul 15, 2014

This is linear permutation. So, 4! = 24 ways they can stand in the line. :)

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Masood Salik
Jul 13, 2014

as order matter.. total arrangment will be 4P4=4!=24

0 Helpful 0 Interesting 0 Brilliant 0 Confused

4 people can stand in a line in 4! ways= 4 3 2*1=24

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Asad Ullah
May 8, 2014

4!=4x3x2x1=24

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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