Rearranging the Photo Line

Probability Level 1

5 5 people are waiting in line for their picture to be taken. How many different ways can the line formed?


The answer is 120.

Arron Kau by Arron Kau

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23 solutions

Rutvik Paikine
Dec 16, 2013

There are 5 choices for the 1st place.

There are 4 choices for the 2nd place.

This continues till we have 1 choice for the last place.

Implying, no. of choices to be 5!.

Hence the answer 120.

12 Helpful 0 Interesting 0 Brilliant 0 Confused

Very well said.

Ameya Salankar - 7 years, 5 months ago

The answer is 120. This is because in the first spot in the queue, there are 5 possible people who can go there. In the second spot in the queue, there are only 4 people who can go there, since one is already in the queue. This continues until the final spot in the queue, where only 1 possible person can go. Hence, the answer is 5×4×3×2×1, which equals 120.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Prasun Biswas
Dec 16, 2013

We have to arrange 5 people in a line and this can be done by permuting 5 people taken all at a time, i.e, 5P5 = 5! = 120

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Yash Maurya
Dec 16, 2013

This can be done by 5! ways so 5! = 5x4x3x2x1=120

2 Helpful 0 Interesting 0 Brilliant 0 Confused

5! = 120 as easy as that

2 Helpful 0 Interesting 0 Brilliant 0 Confused

The ways we form the line is the same as 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120

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Harshal Desai
Dec 17, 2013

5 4 3 2 1 = 120

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Bhavesh Bhagde
Mar 29, 2014

5 4 3 2 1=120

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Philippe Arnoux
Mar 27, 2014

5 ! = 120 solutions différentes.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Iranna Hubballi
Mar 20, 2014

5 4 3 2 1=120

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Francis Solis Jr.
Mar 20, 2014

Simply 5 factorial (5!).! 1st Line-> 5 people 2nd Line-> 5-1=4 3rd Line-> 5-2=3 4th Line-> 5-3=2 5th Line-> 5-4=1 Formula=5 4 3 2 1= 120 different ways.

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'n' objects can be arranged in 'n' places in 'n !' ways. so, here 5 ! = 120 ways.

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Meldrin Rebello
Mar 9, 2014

5! = 120

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Rom Balaga
Mar 5, 2014

There are five(5) place to be occupied by five(5) person.

On the 1st place, the possibility the place will be filled is 5.

On the 2nd, the possibility the place will be filled is 4.

On the 3rd, the possibility the place will be filled is 3.

On the 4th, the possibility the place will be filled is 2.

leaving the 5th place to be occupied by the remaining 1.

the solution would be: (5)(4)(3)(2)(1) = 120

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Arijit Banerjee
Mar 5, 2014

5P5 = 120

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Rishabh Nishad
Feb 27, 2014

5!=120

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Algen Alesna
Jan 24, 2014

using probability/posibility of a person to takes place to other person wihout returning to his place!!!!!! 5 4 3 2 1=120

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Rohan Sharma
Dec 18, 2013

no. of ways will be 5!

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Mario Coelho
Dec 17, 2013

5 4 3 2 1=120 possible ways.

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Nurul Alam Pavel
Dec 16, 2013

number of ways the line can be formed = 5!= 120

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Krishna Gundu
Dec 16, 2013

Let P1, P2.... P5 be the persons.It makes a lot of difference between the P1 standing ahead of P2 and viceversa. So the problem(in simpler words) is asking the number of permutations possible for 5 people and 5 places.

So, the answer is 5P5 or P (5,5) = 5! = 120

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Aries Eroles
Dec 16, 2013

5P5=120

0 Helpful 0 Interesting 0 Brilliant 0 Confused

5c5

Mansi Bhalothia - 7 years, 5 months ago

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No, since the people are being arranged in a line, arrangement and positions of the people in the line is important, so you cannot use combination as it only takes into view the selections of the people and does not count the different arrangements.

Prasun Biswas - 7 years, 5 months ago

5C5=1 is wrong. Just common sense. :))

Aries Eroles - 7 years, 5 months ago

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You have to math sense more than common sense

Krishna Gundu - 7 years, 5 months ago
Rutvik Paikine
Dec 16, 2013

There are 5 choices for the 1st place.

There are 4 choices for the 2nd place.

This continues till we have 1 choice for the last place.

Implying, no. of choices to be 5!.

Hence the answer 120.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

nice idea

sathiya narayanan - 7 years, 5 months ago

Thus answer= 5!=5x4x3x2x1= 120 :)

Haha Low - 7 years, 5 months ago

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