Question

Suppose your statistics instructor gave six examinations during the semester. You received the following grades (percent correct): 79, 64, 84, 82, 92, and 77. Instead of averaging the six scores, the instructor indicated he would randomly select two grades and compute the final percent correct based on the two percents. How many different samples, without replacement, of two test grades are possible

Answer 1

15 samples

Explanation:

The total sample space consists of 6 items

{79,64,84,82,92,77}

So,

n=6

The instructor has to randomly select 2 test scores out of 6.

So, r=6

The arrangement of scores selection doesn't matter so combinations will be used.

`C(n,r)=(n!)/(r!(n-r)!) \\C(6,2)=(6!)/(2!(6-2)!)\\=(6!)/(2!*4!)\\=(6*5*4!)/(2!*4!) \\=(30)/(2)\\=15\ ways`

Therefore, there are 15 different samples are possible without replacement ..