00:01
This problem says a bakery sells six different kinds of pastry.
00:05
If the bakery has at least a dozen of each kind, how many different options for a dozen of pastries are there? what if the box also is to contain at least one kind of each pastry? and to start off to figure out how many options for a dozen for the box there could be, we're looking at this as a combination with repetition.
00:23
And the formula we can use there is combination or choose n plus r minus one, choose r and the n value in this case is the number of different categories or types that we're selecting from and here we had six different types of pastry so that would be combination six plus the r value or the r value is the total number of items that we want to choose and we want to choose 12 and that's minus one and then r again for the number we want to choose so that would be 12 so that gives us combination of 6 plus 12 which is 18 minus 1 to give us 17 and then 12.
01:03
So that's 17 choose 12, which would evaluate to give us the result of 6 ,188 different options we would have.
01:13
Next, we're looking at the same type of problem, but this time we wanted to what if the dozen has to contain one of each type.
01:18
So we can still use the same formula where we have combination n plus r minus one choose r.
01:26
But in this case, we have already selected six of the pastries because we wanted to make sure we had one of each different type.
01:33
So now at this point, what we are looking at is the number n or the number that we are wanting to choose as still being six...