Question

How many groups of ten questions contain at most three that require proof?

a) 1
b) 2
c) 3
d) 4

Answer 1

There are 20 groups of ten questions that contain at most three questions that require proof.

Step-by-step explanation:

The question asks how many groups of ten questions contain at most three that require proof. This can be interpreted as selecting three questions from a group of ten. To find the number of groups, we can use the combination formula:

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

where n is the total number of questions (10) and r is the number of questions that require proof (3). Plugging in the values, we get:

C(10, 3) = 10! / (3!(10-3)!) = 10! / (3!7!) = 10 x 9 x 8 / (3 x 2 x 1) = 120 / 6 = 20

Therefore, there are 20 groups of ten questions that contain at most three that require proof. The answer is a) 1.