ADA Sample QR #38

[dentalknight]

Jill has 6 different books. She will select one book on Monday, and a different book on Wednesday. In how many ways can Jill select two different books?

I know this has to do with combination and stuff, but I'm still a little rusty on that topic. In fact, I don't even really remember using it before studying for the DAT. Can someone explain how to do this using the formula step by step? It would help a lot. Thanks!

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[ksksks]

15?

 

[dentalknight]

thats what i had, but apparently the answer is 30

 

[ksksks]

it really depends upon the wording of the question (which needs be clarified in the question) but 30 could also make sense...

books 1-6

1-2 1-3 1-4 1-5 1-6
2-1 2-3 2-4 2-5 2-6

(6 x 5 = 30)...I thought once you get 1-2, you cant get 2-1...which in that case would be 15.

 

[dentalknight]

well i just know that in order to do this, you have to use the combination method. i am just rusty on that stuff right now. anyone explain it using that method?

 

[Streetwolf]

Oh good it's this question again but worded so much better!

You want two books where ORDER MATTERS. This is clear because she wants one book specifically for Monday and the other specifically for Wednesday. Choosing book A on Mon and book B on Wed is DIFFERENT than choosing book B on Mon and book A on Wed.

Use a permutation (6 P 2) or just do 6 * 5 = 30.

 

[Mamona]

I follow the combination formula like this C= 6! / 2!(6-2)! which answer is 15, but I am always confuse, when do I need to do that formula or this one C = 6! / (6-2)! ?? (which will give the right answer 30.)
Is there any way or specific word or words in the problem that give an idea which one to use!!!
I have done destroyer and I found the same problem they do not explain why they use one or the other one.....

 

[msavaya]

Well for this question, on monday she has 6 books to choose from, and on wednesday she only has 5 books to choose from, because she already took 1 out...So 6x5 gives 30 combinations...

Or, you can do it another way. Anytime they give you a number for a set of things and ask "how many ways can she choose 2" from that set, you just put the total number on top, and how many she wants to choose at the bottom. so 6/2, then you do 6!/(6-2)! which is Permutation. This is simply just 6!/4! which is 6x5x4x3x2x1 all over 4x3x2x1 which gives 720/24, which equals 30 different ways.

Hope that helps.

 

[Streetwolf]

I follow the combination formula like this C= 6! / 2!(6-2)! which answer is 15, but I am always confuse, when do I need to do that formula or this one C = 6! / (6-2)! ?? (which will give the right answer 30.)
Is there any way or specific word or words in the problem that give an idea which one to use!!!
I have done destroyer and I found the same problem they do not explain why they use one or the other one.....

Did you not read my post?

Use perm when order matters and use combo when order does not matter. If Jill just wanted to pick 2 books to read at any point, then you'd use a combination because it doesn't matter if she pulls book A out first and book B out second, or vice versa. She just wants to pull 2 books out.

 

[msavaya]

Oh and I forgot the mention the shortcut to permutation.... If for example you used 6!/(6-2)!, you can easily cancel out many numbers... 6x5x4x3x2x1 / 4x3x2x1, you can see what the top and bottom have in common, and cancel them out...so you are left with 6x5 = 30.

 

[Mamona]

Did you not read my post?

Use perm when order matters and use combo when order does not matter. If Jill just wanted to pick 2 books to read at any point, then you'd use a combination because it doesn't matter if she pulls book A out first and book B out second, or vice versa. She just wants to pull 2 books out.

I think I got it now.
Your post came after my post.......Anyway thanks that make so much sense now