Suppose your statistics instructor gave six examinations during the semester. You received the following grades (percent correct): 89, 64, 88, 89, 91, and 75. Instead of averaging the six scores, the instructor indicated he would randomly select five grades and compute the final percent correct based on the five percents.

(a) How many different samples, without replacement, of five test grades are possible?

35

15 6C2=6!/(2!(6-2)!)=15

Oops it's 6

6!/(5!x(6-5)!)

To determine the number of different samples of five test grades that are possible without replacement, we can use the concept of combinations.

The formula for calculating combinations is given by:

C(n, r) = n! / (r!(n - r)!),

where n is the total number of items and r is the number of items selected.

In this case, we have six test grades and we want to select five of them. Using the formula, we can calculate the number of different samples as:

C(6, 5) = 6! / (5!(6 - 5)!) = 6! / (5! * 1!) = 6.

So, there are 6 different samples of five test grades possible without replacement.