Math question

Discus: SAT/ACT Tests and Test Preparation: April 2004 Archive: Math question
 By Lisasimpson (Lisasimpson) on Thursday, April 29, 2004 - 09:13 pm: Edit

hey..this question is in the math part of kaplan 1600 and i dont get it

alex wishes to plant 3 diff. fruit trees in his front yard. he has 5 diff. types he can choose from: cherry, plum, apple, peach, and pear. how many different combinations of fruit trees are possible?

it says in the back to list out all the possibilities and that there are 10. but i remember learning something like this in school where it was like a permutation or a combination and we multiplied 5 x 4 x 3 to get the answer...can anyone clear this up for me?

 By Crypto86 (Crypto86) on Thursday, April 29, 2004 - 09:19 pm: Edit

Since order doesn't matter, we can use 5 nCr 3 (for 5 possible items and 3 at a time). Plugging this in a calculator indeed gets 10.

 By Daromanian (Daromanian) on Thursday, April 29, 2004 - 09:26 pm: Edit

5*4*3*2*1 / (3*2*1 * 2*1)

 By Lisasimpson (Lisasimpson) on Thursday, April 29, 2004 - 09:26 pm: Edit

hmm yea i get that its a combination, but at school we did it by setting up three blank lines for the 3 fruit trees wanted:

___ x ___ x ___

then for the first space, there're 5 possibilties, 4 possiblities for the second space, and 3 possibilities for the third space...multiplying them gives 60..why doesnt this work?! i'm still soo confused

 By Crypto86 (Crypto86) on Thursday, April 29, 2004 - 09:31 pm: Edit

That's if order matters, but it doesn't explicitly say that it does.

 By Crypto86 (Crypto86) on Thursday, April 29, 2004 - 09:31 pm: Edit

That's if order matters, but it doesn't explicitly say that it does.

 By Haithman (Haithman) on Thursday, April 29, 2004 - 10:29 pm: Edit

Ah! so thats what that nCr thing is for! Wow so I can use that on all combination problems? Any other tricks I can use with my TI?
Thank You

 By Brum (Brum) on Thursday, April 29, 2004 - 11:03 pm: Edit

can you give an example of a permutation problem please?

 By Jens (Jens) on Thursday, April 29, 2004 - 11:14 pm: Edit

ill take a stab at it

order does NOT matter for ex: cherry plum apple is the same as apple plum cherry. so you have to use combonation as stated above.

order DOES matter for permutation problems- something like how many diff combos of 3 people in a 2 seat car (not including the driver) thus:
A B is diff from B A b/c of the seating (person A is in the first seat in AB whereas person B is in the first seat in BA- thus the two 'cases' are diff & order matters.) so in this case it would be 3*2*1 or permutation.

hope it makes sense

 By Haithman (Haithman) on Friday, April 30, 2004 - 01:18 am: Edit

Wow this just made the Math section that much easier/faster.
Thank You

 By Crypto86 (Crypto86) on Friday, April 30, 2004 - 11:45 am: Edit

Yah - same with factorials (4! for example). On problems like "how many arrangements are there with 3 different cars and an empty space out of 4 total spaces", you would treat each car as 1 different item AND the empty space as one different item (to make it follow the example). By definition, the permutation arrangement of n items is n!, so since you have 4 items it would be 4! (4*3*2*1) and boom, 24 total possibilities. Sure beats writing them all down!