Please explain combinations and permutations?

A "Combination" and a "Permutation" are ways of finding out how many ways a group can be organized.

Simply put

Combination - order does NOT matter

Permutation - order DOES matter

Here's some examples of both:

Imagine there are 4 friends Andy, Erin, Jim, and Pam going to a movie. Don't know if you watch the office, but I'm a huge fan, so I figured I'd throw some familiar names in.

A combination would be the group wants popcorn and drinks, and 2 people have to go in order to carry it all. The question would be how many ways could the group of 2 change.

Order doesn't matter in this example, because Jim, Andy would be the same as Andy, Jim. This means this is considered a combination. IF you were to list it (this is just for due diligence's sake) it would be (Andy, Erin) (Andy, Jim) (Andy, Pam) (Erin, Jim) (Erin, Pam) (Jim, Pam). There are 6 ways that 2 people can be picked from the total of 4.

ANSWER = 6

While listing works for a short example like this one, it would be far to time consuming to use on larger sets, such as how many ways there are to pick 4 winners of a raffle which had thousands of entrants. There are easier ways to do this, and here is how to set this up, you must use the formula that your teacher gave you. There are 2 ways I know how, using the notation nCr with a TI or other graphing calculator, and the second formula (n!)/(r! (n-r)!). I know that the letters are intimidating, but its really easy. N = the total number in a group, in our example, n = 4. R is the number picked from the group, in this case 2, so R = 2. the ! means factorial. e.g 4! = 4 x 3 x 2 x 1

so to solve, just plug and chug.

(4!)/((2!)(4-2)!)

(4 x 3 x 2 x 1) / ((2 x 1) (2 x 1))

24 / 4

6

A permutation would be a question like how many ways can the four people sit down. In this example order does matter, because (Jim, Pam, Erin, Andy) is not the same as (Jim, Pam, Andy, Erin). They are counted as separate results. Permutations are much easier in general. To solve, simply take the factorial of the total number of the group, or n!.

For this example, it would look like this:

4!

4 x 3 x 2 x 1

24

Another way of thinking about permutation is to draw the scenario and fill in the blanks and multiply at the end, like this.

__ x __ x __ x __ with each blank representing one square. There are four seats, so there are four blanks.

To fill in the blanks, think of how many options are available to sit in each seat.

__ ( Jim, Andy, Pam, Erin) x __ (Andy, Pam, Erin) x __ (Pam, Erin) x __ (Erin) or 4 x 3 x 2 x 1

I hope this long winded explanation is helpful, and don't feel shy to ask questions. Also, your teacher may yell at about asking questions during class, but if you go after class or to any extra time she they set aside, I'm sure your teacher would be more than willing to help. Their job is to teach you math, they want you to learn. Take some initiative and be the best student you can be.

Permutation And Combination Explanation

I studied this in Math final unit, yet i'm in grade 7 so what I found out won't be as complicated as what you're analyzing. For starters, you are able to desire to understand the version between variations and mixtures. mixture are whilst order would not rely, like once you're ingesting a fruit salad. you would be able to desire to declare there are "bananas, apples, and pears in my salad" or "Apples, pears, and bananas" it is not appropriate through fact the order you assert it in describes a similar ingredient anyhow. whether.. variations is whilst order does rely, like a pin extensive style. a mixture equation could be nPk over r factorial. ok yet considering that your difficulty spot is variations... Say the question is "In how many techniques can a president, vice chairman, and secretary be chosen from a class of 30 pupils?" to remedy, you would be able to desire to understand a thank you to set this up in an equation. or nPk. n is the entire style of issues interior the concern, subsequently 30 (30 people working for the region). so so a techniques we've 30Pk. P only skill permutation ok is the entire style of folk who're truly getting used, so subsequently, 3 considering that there can in ordinary terms be one president, vice chairman, and secretary (3 positions in entire). so now the concern is 30P3 from there you in ordinary terms use 30 like a factorial, yet in ordinary terms factorialize thrice...? if it truly is clever! You get the three from the style of positions. so truly 30x29x28 to get a entire of 24, 360 outcomes. yet differently to recollect it truly is 30 factorial over 27 factorial. You get the 27 from 30(the entire # of folk)-3 (the style of positions obtainable). Simplify that, and you get a similar answer:24, 360 outcomes. If it truly is annoying to remember, only think of that for the period of ordinary terms a million individual out of 30 can get the region as president, that leaves 29 people who could desire to be vice chairman, then after that grew to become into chosen, 28 who could desire to be secretary. wish you get it now!

I thought you wrote permutations the order DOES matter,

then later on you wrote it is just 4! because it does not matter.