Help with combination/permutation problem?

opg98

New member
Joined
Sep 24, 2017
Messages
1
I have a permutations/combinations problem that I can't figure out at all. I desperately need help.

"in how many ways can the letters of the website MySpace be arranged if all of the letters are used and the vowels a and e must always stay in the order ae?"

I've tried writing "blanks": ie. The first blank, we have 7 letters we can use, the second blank we have 6 letters left, and so on.

but the part about "ae" having to be in the order "ae" is confusing me. I've tried to count "ae" as one letter or blank, as instructed by a tutor, which is only confusing me more.

(Overall, I seem to have a problem with permutations and combinations. I can't even tell when I'm supposed to use a permutation formula or a combination one because sometimes it seems like order matters when it doesn't at all. I'm totally lost. My professor says there's four ways of solving these problems.

Either we can 1) use factorials/ multiplication principle and "blanks", 2) use the calculator (i.e. 4 NPR 4) or formula, 3) draw a diagram or 4) add them (i.e. We had a problem about a quorum having a minimum of 7 members, and we needed to find the number of ways a quorum could be formed if there were 13 members in a group. So we added C (13,7) + C (13,8) + C (13,9 + C (13,10) and so on.)

however it seems whenever I use one of these methods to solve a problem, it ends up being the wrong one. in the end, I don't think I really understand how to approach these problems or solve them. I know I have the basics down (like how with permutation, order matters and with combinations, order doesn't.) but from that point on, I'm hopeless.)
 

tkhunny

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Staff member
Joined
Apr 12, 2005
Messages
10,097
Well, it's not really possibly to get you there by magic. You just have to grow in your thinking. One thing that helps me along the way is this a simple thought.

Normally, we hear this:

Permutations - Order Matters
Combinations - Order is of no consequence. It's just a collection of things.

123 is a combination of three digits

123 - One permutation of the combination 123
321 - One permutation of the combination 123
231 - One permutation of the combination 123
213 - One permutation of the combination 123

The simply idea is just this, given a set of at least two objects, there are more permutations than combinations.
 
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