QR question, help please!

[JakeMUSC]

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Hey, I know how to find the answers (but after wasting 5 minutes) to these type of questions, but there should be an equation I could use. EX:

Jill has six different books. In how many ways can Jill select two different books?
A. 36
B. 30
C. 18
D. 15
E. 12

This ones easy and I used logic to find 30 in about 20 seconds, but what if its like this:

Jill has six different books. In how many ways can Jill select three different books?

Im guessing you smart math geniuses have some sort of actual process to find this out.
THANKS FOR YOUR HELP!!!!

 

[DrTacoElf]

Combination/Permutation

http://mathworld.wolfram.com/Combination.html

http://mathworld.wolfram.com/Permutation.html

Slight Variation (circular permuation)

http://mathworld.wolfram.com/CircularPermutation.html

Any of these 3 concepts can pop up on the DAT as well as the binomial formula which would be applicable for the last case you posted (i'll leave that up to someone else as I have forgotten it).

 

[JakeMUSC]

Dr. Taco Elf, thanks for the links buddy!

Ok, so now my new question is. The formula gives an answer of 15. Which is what I came up with using my shorthand. So I guess these types of questions consider the combination of 1 and 6, different than 6 and 1, therefore making a total of 15X2= 30 combinations, (which is the posted answer). Hmmm, I d like to talk to someone from ADA, lol.

 

[DrTacoElf]

Dr. Taco Elf, thanks for the links buddy!

Ok, so now my new question is. The formula gives an answer of 15. Which is what I came up with using my shorthand. So I guess these types of questions consider the combination of 1 and 6, different than 6 and 1, therefore making a total of 15X2= 30 combinations, (which is the posted answer). Hmmm, I d like to talk to someone from ADA, lol.

1 and 6 versus 6 and 1 is essentially a combination versus a permutation. Permutation considers each different, combination does not.

 

[JakeMUSC]

So, was the question I posted a permu or comb?

 

[luder98]

Hey, I know how to find the answers (but after wasting 5 minutes) to these type of questions, but there should be an equation I could use. EX:

Jill has six different books. In how many ways can Jill select two different books?
A. 36
B. 30
C. 18
D. 15
E. 12

This ones easy and I used logic to find 30 in about 20 seconds, but what if its like this:

Jill has six different books. In how many ways can Jill select three different books?

Im guessing you smart math geniuses have some sort of actual process to find this out.
THANKS FOR YOUR HELP!!!!

It's the combination of 2,6. The formula is 6!/(2!*4!). 4 is from 6-2. Cancel the 4! at the bottom with 6! on the top, you get 5*6/2 which is 15, not 30. Now you try the formula with the second portion🙂 It should be 20. Good luck.

If you want to make it a permuation problem, here is how it will read: How many ways can the person ARRANGE his two (or three) of his books from 6 different books. Permutation deals with order while combination does not consider order. Thus, the formula for permutation would be n!/(n-k)!. The k! is not in the formula as in the comb case.

A special case of permutation is called circular permutation. And the reduced formula in this case would be (n-1)!/(n-k)!. There is a problem in tsp asking how many ways can you sit 6 people around a circular table. In this case n=6, k=6. Apply to the formula the result is (6-1)!/(0!)=5! which is equal to 120.

I only scored 20 on math. Can you believe it? Shame on me 😳

 

[luder98]

Any of these 3 concepts can pop up on the DAT as well as the binomial formula which would be applicable for the last case you posted (i'll leave that up to someone else as I have forgotten it).

For equation ax^2 + bx + c = 0, the solutions of the equation are

(-b +/- sqrt(b^2-4ac))/(2a), given b^2-4ac is positive. If not, there is no solution. If zero, one solution which is -b/(2a).

A special case is when b is an even number. First calculate b'=b/2. The solutions are then

(-b'+/-sqrt(b'^2-ac))/a, again, given b'^2-ac is positive.

PS: b' is not the derivative of b. I used it for naming purpose only.

 

[DrTacoElf]

Actually this is the one I was referring to

 

[luder98]

Actually this is the one I was referring to

My bad. I thought you meant quad formula. I was wondering how u post those characters 😀

 

[DrTacoElf]

My bad. I thought you meant quad formula. I was wondering how u post those characters 😀

Mine is actually a .jpg picture from another site.

 

[justsusan]

you guys are making this out to be more complicated than it is.

Jill has 6 books so she has 6 choices for book 1. she has 5 choices left for book 2. she has 4 left for book 3.

so 6x5x4 ways.

 

[luder98]

Mine is actually a .jpg picture from another site.

I know. It's a .gif file. I saw it when I clicked reply. You seem to navigate the web pretty well🙂

 

[luder98]

you guys are making this out to be more complicated than it is.

Jill has 6 books so she has 6 choices for book 1. she has 5 choices left for book 2. she has 4 left for book 3.

so 6x5x4 ways.

This is incorrect. The concept you use is for probability. For example, what is the probability of drawing three spades in a row from a deck of cards. That would be 13/52 times 12/51 times 11/50.

 

[DrTacoElf]

Yeah he was thinking 6! but since we are dealing with 2 books you can't do that.

 

[justsusan]

oh yeah. order doesn't matter. oops. so much for discrete math.