rooshandark8: Show me work for Question 3,8,9 and 13 or explain how you got the answer (For those that don't know, in selecting
k items from a group of
n, the difference between permutations [P(n,k)] and combinations [C(n,k)] is that in permutations, order matters. In combinations, it does not.)
P(n, k) = n! / (n-k)!
C(n, k) = n! / (k! * (n-k)!)
3. Based on the graphs in other problems, we assume the blue colored region to the right of -3 is the area of interest. A closed dot indicates -3 is part of the solution. Therefore, (
C) x ≥ -3
8. There are 9 letters in the word
seventeen, however, only 5 of them are unique; there are 4
e's and 2
n's. This means that while there are 9! ways to arrange the letters, a significant number of those rearrangements are redundant. In every rearrangement, the
e's and
n's can be shifted around, in 4! ways and 2! ways, respectively. Since this occurs in every arrangement, they are divided out. 9! / (4! * 2!) = (
B) 7,560
9. The question is unclear as to whether order matters on this test. However, given that P(12, 10) = 12! / (12-10)! = 239,500,800 does not appear among the answer, we must assume it does not. Therefore, the answer is C(12, 10) = 12! / (10! * (12-10)!) = 12! / (10! * 2!) = (
B) 66
13. C(100, 2) and C(100, 98) both describe the exact same problem. Think about it in terms of splitting a group of 100 items into 2 groups: If you choose 2 items out of 100, then you are by definition leaving behind a second group, 98 out of 100, and vice versa. Therefore, if C(100, 2) is defined as 4,950, then C(100, 98) is (
A) 4,950