how many ways can a person select 5 glazed doughnuts, 4 cake doughnuts, and 3 filled doughnuts from a selection of 13 glazed doughnuts, 10 cake doughnuts, and filled doughnuts?
It would help if you proofread your questions before you posted them.
From how many filled doughnuts?
To find the number of ways to select doughnuts, we can use combinations. A combination is a selection of items where the order does not matter.
In this case, we need to find the number of ways to choose 5 glazed doughnuts from 13, 4 cake doughnuts from 10, and 3 filled doughnuts from the available options.
The number of ways to choose the glazed doughnuts can be calculated using the combination formula "nCr," where n is the total number of options and r is the number of items to be chosen.
So, the number of ways to choose 5 glazed doughnuts out of 13 is:
C(13, 5) = 13! / (5! * (13-5)!) = 1287
Similarly, the number of ways to choose 4 cake doughnuts out of 10 is:
C(10, 4) = 10! / (4! * (10-4)!) = 210
And the number of ways to choose 3 filled doughnuts from the available options is:
C(filled doughnuts, 3)
Therefore, the total number of ways to select the desired combination of doughnuts is the product of the ways to select each type:
Total ways = C(13, 5) * C(10, 4) * C(filled doughnuts, 3)
Please specify the number of filled doughnuts available to complete the calculation.