00:01
So this question is asking us to evaluate the following expression.
00:04
So let's first quickly review what this means.
00:07
So in the general form, if we have an expression n -pr, what this means is that if we have a set of n objects and we want to arrange r of them, such that the order doesn't matter, then we can use the following expression, where it's n factorial over n minus r factorial.
00:31
So what we're going to do is we're going to evaluate these four expressions then using this formula.
00:36
So if we have 8p2, that means 8 factorial over 8 minus 2 factorial.
00:45
So when we do this, we can further simplify this first so that it's easier for us to calculate.
00:51
So 8 minus 2 is just 6.
00:53
And then since factorial, we can simplify the 8 factorial down to 8 times 7 times 6 factorial.
01:01
Since six factorial is just six times five times four times three times two times one.
01:06
So we can use this as a way to simplify our expression.
01:09
So we can cancel out these six factorials.
01:12
And we're left with eight times seven, which is just 56th.
01:16
So now we're going to do a similar thing for the rest of these questions.
01:20
So the 7p5 is just 7 factorial over 7 minus 5 factorial...