00:01
Here on this problem, we are told that we have a batch of pills, seven of which are good, and three are defective.
00:06
And so we have seven good pills, and we have three defective pills.
00:17
Now, it's important to note here, as simple as it may seem, that that means that we have 10 total.
00:23
So, n is equal to 10.
00:26
Now, first, we want to know how many different permutations are possible when all 10 pills are randomly selected without replacement.
00:33
And we want to know how many different permutations are possible when all 10 are random mutations.
00:39
Automatically replacement.
00:42
Now this is similar to the bookkeeper problem, the bookkeeper problem, or the mississippi problem where you have repeats and so you have to divide by factorials in order to account for the repeats because we have seven that are good.
00:55
And so it's like we've got seven gs and then three defective and so it means we've got three d's for defective.
01:04
That's we want to know how many different ways we can rearrange these letters.
01:08
Well we have ten letters and so there's 10 -factorial ways that we can rearrange them.
01:13
But we do have repeats here.
01:15
And so we've got 7 gs.
01:16
So we need to divide by 7 factorial.
01:18
That'd be the number of ways of arranging the gs.
01:21
And then we also need to divide by 3 factorial because there are 3ds.
01:25
And that's how many ways we can rearrange the ds.
01:30
Now we evaluate this.
01:34
So this is 10 times 9 times 8...