00:01
We have some combinations questions here.
00:02
The formula for combinations is n factorial over r factorial n minus r factorial.
00:10
So question 6, 12 choose r is 792.
00:18
So 12 factorial over r factorial 12 minus r factorial is 792.
00:26
2.
00:27
Okay, so this would be really, really complicated if you tried to solve it algebraically.
00:33
The best thing to do here is to use trial and error.
00:36
So this is quite a large number.
00:38
I'm going to put in 4 and see what happens.
00:41
So what is 12 choose 4? 495.
00:46
Not quite there.
00:47
Let's try 12 choose 5.
00:49
That's 792.
00:51
So r could be 5.
00:55
That's not here, so we're going to go for the symmetric value of 7, which is option b.
01:05
So if i draw the first couple of layers of pascal's triangle, so that looks like this, you can see the symmetry here.
01:18
So for example, this is 3 choose 0, 3 choose 1, 3 choose 2, 3 choose 3.
01:25
You can see 3 choose 1 and 3 choose 2 have the same value.
01:29
And if i go for the next line, there's symmetry here as well.
01:33
So this is 4 choose 1, 4 choose 2, and 4 choose 3.
01:39
1 and 3 have the same value.
01:41
So if these add up to n, they get the same combinations value.
01:50
Question 7, we want 12 choose 5.
01:54
Oh, well, we don't need to do that.
01:56
I know it's 792.
01:57
If 12 choose 7 is 792, 12 choose 5 is also 792.
02:03
That must be option c.
02:07
8.
02:10
Okay, n choose n.
02:13
N choose n is always 1...