Math D(2010) test 1 #14

[Dental2000]

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In How many ways can 5 people stand in a line?

The answer says P(5,5)= 5! = 120

Wft is P(5,5) and how the heck is it equal to 5!?

 

[tudyfrutie]

How can 5 people stand in line for 5 spaces where order matters

permutation formula: p(n,r) = n!/(n-r)! = P(number of people, number of spaces)

5!/(5-5)! = 5!/0! = 5!/1 = 5 x 4 x 3 x 2 x 1 = 120

 

[Josh779]

where order matters

What does this mean? I keep hearing it but I don't understand why order matters. Isn't multiplication commutative?

 

[LetsGo2DSchool]

Wft is P(5,5) and how the heck is it equal to 5!?

It's like: how many Po--- does it take to change a light bulb--oh never mind.

 

[LetsGo2DSchool]

What does this mean? I keep hearing it but I don't understand why order matters. Isn't multiplication commutative?

Think of it as 5 girls you want to date:

Blonde - A
Brunette - B
Redhead - C
Slut -D
Freak -E

But you have preferences so order does matter.

Your scorecard lineup could look like:

A, B, C, D, E
A, B, C, E, D
A, C, B, D, E
A, C, B, E, D
A, D, B, C, E
A, D, B, E, C
B, A, C, D, E
B, A, D, C, E
B, A, E, C, D
.... and so .....

In the end you'll have 120 different possibilities.

 

[Cappi]

Say like....at your work place. There are currently 10 people there. You want to find out how many ways can you have president, vice president, and a secretary. Order would matter in this case. You would do this problem with permutation: P(10,3).

Say you want to get a group of 3 people in this project you are working on. It doesn't matter who gets pick first or last. So order does not matter. You would do this problem with combination: C(10,3)

Ultimately, you will have more Permutation than Combination. Since a Combination of [x,y,z] you will have Permutations of x-y-z, x-z-y. z-x-y, z-y-x, y-z-x, y-x-z

Locker Combination should be named locker permutation instead. Since 7-13-4 does not equal 4-13-7. Order matters

hope this helps