00:01
Okay, so we have first six spots, one for the plain croissons, one for the cherry croissons, another one for the chocolate, almond, apple and broccoli croissant.
00:17
We have 12 croissons to play there.
00:21
So for example, this will mean that we bought two plain croissons, two cherry croissons, one chocolate one, one almond, two apple and two plain two cherry one chocolate one almond two apple and four broccoli so here we have one line missing extra see one two three four five and here on top we have five lines okay so we have to organize these five lines and twelve stars that means seventeen of so we have 17 spots and 12 of them are going to have stars.
01:10
So that will be 17, take it 17 combinatorial number with 12.
01:16
And that is 17 factorial over 12 factorial, 5 factorial.
01:20
That gives us that number.
01:23
Now for the second one, we have to place 24 croissons these times.
01:29
So we will have to order 41 elements.
01:33
And we have 41 spots that we can choose.
01:39
I'm sorry, not 36 croissons, because it's three dozens.
01:44
So we have to choose 36 of them.
01:47
So that would be the combinatorial number 4136 that gives us that result.
01:54
Now for part c, we are going to consider first when we don't choose any croissant, any broccoli croissant.
02:03
So we are choosing now, we have five spots instead of six, meaning that we have four lines and 24 croissons.
02:16
So say, for example, in this case, we have still again one line extra.
02:24
Let me remove this one.
02:26
So we'll have two croissons, plain croissons, two cherry croissons, two chocolate croissons, two almond croissants, four apple croissons, and no broccoliero.
02:41
Okay, so that's one case in which we can order these 28 elements.
02:48
We have 28 spots and 24 of them are going to be selected to put the stars.
02:54
That gives us the combinatorial number 2824.
02:58
And that's the result for that.
03:00
Now, what if we get only one broccoli croissant? so we will have again five places to choose, and now we will be placing 23 croissons because the 24 is already placed for the croissant.
03:16
So this is the same example than before.
03:21
Actually exactly the same, let's remove this one.
03:24
So we will have choose in this case, two plain croissons, two cherry croissons, two chocolate croissons, two almond, three apple, and one broccoli that is not in drawing.
03:42
So how many ways we can do that? we have 27 elements, 27 spots, and 23 are going to be selected to have the stars.
03:51
So that is the combinatorial number 2723.
03:55
That is that value.
03:57
Now we have one last option is when we choose two broccoli croissons.
04:02
So again, we have five places and 22 croissons to choose...