List the sample space for rolling two dice and finding the sum of the numbers. how many 8's are there in the sample space? [assume that rolling a 3 and a 5 is the same as rolling a 5 and a 3.] a) 2 b) 3 c) 4 d) 5

Using the given assumption, there are 3.

The sample space for rolling two dice and finding the sum is:

2   3   4   5   6    7 
3   4   5   6   7    8
4   5   6   7   8    9
5   6   7   8   9    10
6   7   8   9   10  11
7   8   9  10  11  12

From the sample space alone, there are 5.  However, since a 3 and a 5 is the same as a 5 and a 3, this means that 2, 6 is the same as 6, 2 as well; this takes 2 off of the 5, leaving us 3.

The answer would be 27 because assuming that each package has 1 bar of soap and 1 tube of toothpaste, after 27 packages they would run out of toothpaste