Official ACT question- June 2010

Test Preparation ACT Preparation
1

<p>I suck at probability and was wondering if you guys could help me out on this question. If you've got the June 2010 test it is question 31.</p>

<p>"Kayla offers to sell 2 of the 25 pieces of candy to her brother Virgil. She lets Virgil have a choice of 2 pieces of the same candy item on 1 piece each of 2 different candy items. Kayla will have Virgil pay the same total cost for the 2 pieces that he would pay at the Laszko's (the name of the candy store). How many different total costs are possible for Virgil's 2 choices"?
(The question has a chart with 4 candies and lists different prices for each)
A. 8
B. 10
C. 12
D. 14
E. 16</p>

<p>the Answer is B. Please explain how to get the answer.</p>

2

<p>You could do
xx xy xz xw
yy yz yw
ww wz
zz</p>

3

<p>UVA
isn’t there a formula that could be used here?Or,do we physically count the possibilities as you’ve shown?</p>

4

<p>I think I got it.This is the formula,correct?
(n+r-1)!
-------- = 10
r!(n-1)!</p>

5

<p>thanks a lot! Can you please tell me what n and r stand for</p>

6

<p>‘n’ is the number of things to choose from(in this case it was 4 candy prices)
‘r’ is the number chosen(you had to choose 2 of the 4 candy prices,so 2 in this case)</p>