My couch potato friend enjoys sitting in front of the TV and grabbing handfuls of three chocolates at random from his snack jar. Unbeknownst to him, I have replaced 1 of the ten chocolates in his jar with a cashew. (He hates cashews with a passion!) How many possible outcomes are there the first time he grabs three chocolates How many of these include the cashew

A)120 outcomes, and 12 include the cashew
B) 242 outcomes, and 36 include the cashew
C) 120 outcomes, and 36 include the cashew
D) 720 outcomes, and 72 include the cashew
E) 84 outcomes, and 12 include the cashew

Question

My couch potato friend enjoys sitting in front of the TV and grabbing handfuls of three chocolates at random from his snack jar. Unbeknownst to him, I have replaced 1 of the ten chocolates in his jar with a cashew. (He hates cashews with a passion!) How many possible outcomes are there the first time he grabs three chocolates  How many of these include the cashew 
 
A)120  outcomes, and 12 include the cashew
B) 242 outcomes, and 36 include the cashew
C) 120  outcomes, and 36 include the cashew
D)  720 outcomes, and 72 include the cashew
E) 84  outcomes, and 12 include the cashew

Quizplus · Accepted Answer

The number of possible combinations of three chocolates from a set of ten is given by "10 choose 3," which equals 120. Out of these 120 outcomes, there are 9 ways to choose three cashews (since there are only 9 cashews), and there are 27 ways to choose two chocolates and the one cashew. Therefore, the total number of outcomes that include the cashew is 9 + 27 = 36.

My Couch Potato Friend Enjoys Sitting in Front of the TV