00:01
Here on this problem, we are told that we have a test with 20 true and false questions.
00:05
And we want to know how many different ways in a student complete this test.
00:11
Now there are two options for each test, and then there are 20 questions total.
00:17
And so it means there are two to the 20th total ways that this test can be completed.
00:22
Two options for each, and then 20 total.
00:26
And so we just need to evaluate 2 to the 20th.
00:29
And this gives us 104, 85 ,7.
00:37
I mean, there's 1 ,048 ,576 total ways to complete this test.
00:46
Now, in b, we want to find the number of ways that a student can answer exactly 10 questions correctly.
00:53
Now we have 20 questions, and we want to choose 10 of them.
00:58
Okay, we're going to answer 10 of them correctly.
01:00
And so this is just 20 choose 10.
01:02
And so this is 20 factorial over 10 factorial, 10 factorial...