00:01
So in this problem where we have 15 questions and we get to choose any 10, to me that tells me that we have a combination happening.
00:12
And the reason why it's a combination is that the order doesn't matter.
00:18
For instance, like, i'm not going to write out all these, but let's say you do numbers one, two, three, maybe you skip four and so on and so forth.
00:34
Assuming everything else is the same, it would be the same as if you did one, then five, and then you went back to two and three, and you did it in a different order, you're still doing the same 10 questions.
00:47
So that's part of part a, and how many ways can the 10 questions be selected, that you would do 15.
00:56
May i don't do this in green because it's kind of the meat.
00:59
It's 15 combination 10.
01:01
And how you do the combination now is 15 factorial over the second number factorial, and then you subtract the two numbers, 15 minus 10 is 5 factorial.
01:13
If you have a calculator that does this, it would be nice.
01:18
13 times 12, but you can actually stop right here because you hit 10 factorial, which would cancel out with this 10 factorial, but that doesn't really cancel out the other pieces.
01:32
But, you know, 5 times 3, each.
01:34
Equals 15 and see four times well two goes into 14 seven times and four goes into 12 three times so you can just type in your calculator seven times 13 times three times 11 i'll hopefully end did this all correctly i got three thousand and three yeah i can double check with my calculator if i because my calculator does this kind of stuff by typing in 15 c 10 i got the same answer.
02:12
Now, in letter b, very different because they say that you have to choose two of the first three problems.
02:20
So there's two of the problems of the 10 that we did earlier...