probability question

[demonicr]

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on the question asking...

jill has six different books. In how many ways can jill select two different books?

the answer says 30

but shouln't it be solved by (6*5)/(2*1)

which equal to 15, this question was on the 2003 dat application booklet so therefore i assume their answer is correct. but i don't get it. i even did it the long way by counting it, and still get 15, can someone please help..
thanks

 

[coodoo]

lets see

6! / 2!(6-2!) = 15

there are a ****load of mistakes on that dat packet it seems

 

[CJMPre-Med]

n/m 😛

 

[demonicr]

lets see

6! / 2!(6-2!) = 15

there are a ****load of mistakes on that dat packet it seems

thanks again, i can't believe the dat packet actually has mistakes, i hope their answers for the actual dat has none..

 

[dane4695]

What's funny about this is this same questions is in the barron's book, except jill is kate.

Interestingly enough, they say its 15 🙂

 

[JayMiranti]

lets see

6! / 2!(6-2!) = 15

there are a ****load of mistakes on that dat packet it seems

could u explain the reasoning behind that calculation? or just memorize that formula? i had trouble on this one too

 

[JavadiCavity]

I think the answer is 30 because the problem doesn't ask for how many UNIQUE ways that two books can be taken. Therefore, you could pick book A first and book B second in one set, but then you could also pick book B first and then book A second in another set. Since order IS important, you have 30 different possibilities.

Mathematically:

First pile: 6 books
Second pile: 5 books

6 * 5 = 30

If ORDER isn't important in the problem, then the answer would be 15 because using my example above, both AB in a set would be equivalent, regardless of whether or not you choose A first or B first.

Mathematically:

(6*5)/(2*1) = 15

 

[demonicr]

I think the answer is 30 because the problem doesn't ask for how many UNIQUE ways that two books can be taken. Therefore, you could pick book A first and book B second in one set, but then you could also pick book B first and then book A second in another set. Since order isn't important, you have 30 different possibilities.

Mathematically:

First pile: 6 books
Second pile: 5 books

6 * 5 = 30

If ORDER is important in the problem, then the answer would be 15 because using my example above, both AB in a set would be equivalent, regardless of whether or not you choose A first or B first.

(6*5)/(2*1) = 15

i think you're right. reading the question closely, it asked, "how many ways the books can be selected?". i guess if it asked, "how many combination of two books", or "how many different sets of two books is picked out". it will be 15
Mathematically:

 

[coodoo]

i think you're right. reading the question closely, it asked, "how many ways the books can be selected?". i guess if it asked, "how many combination of two books", or "how many different sets of two books is picked out". it will be 15
Mathematically:

I'll be damned, you're right. SHould've read the question more carefully. I didnt see anything like that on the real deal, so dont worry about it

 

[JavadiCavity]

I'll be damned, you're right. SHould've read the question more carefully. I didnt see anything like that on the real deal, so dont worry about it

Simple oversight, I do it all the time.

 

[ems5184]

So are you guys saying that because it doesnt ask for UNIQUE ways to pick 2 books that the permutations formula should be used instead of the combinations formula?

The way I interpreted it was to use the permutations formula (getting an answer of 30) because the questions is asking how many ways can you get 2 DIFFERENT books implying that order does not matter.

For this problem, picking books A and B is the same as picking books B and A. Therefore, permutations should be used, right?

 

[JavadiCavity]

I often get confused about order. The way I think of order is this:

Order DOES matter: this means that it is important to determine the order the objects are selected. Hence, AB qualifies as one set and BA qualifies as another set.

Order DOESN'T matter: this means you ignore the order that the objects are selected. Therfore, AB is equivalent to BA.

Hope that helps.

 

[ems5184]

Yea, Javadi, thats how I think of it too.
Glad to see we are using the same reasoning. 👍