How many ways can a person select four books, two CDs, and one DVD from ten books, twenty CDs, and five DVDs?
To handle this type of question, my must be familiar with the C(n,r) notation.
The person can select the books in C(10,4) or 210 ways
the CD's in C(20,2) or 190 ways
and the DVD's in C(5,1) or 5 ways.
So the number of ways to make the selection is
210*190*5 ways or 199500 ways.
Well, let's see. If we have 10 books, we can select 4 in (10 choose 4) ways. If we have 20 CDs, we can select 2 in (20 choose 2) ways. And if we have 5 DVDs, we can select 1 in (5 choose 1) way. So, the total number of ways to make these selections is... drumroll, please... (10 choose 4) * (20 choose 2) * (5 choose 1). Now, I'm going to grab my calculator. It's just around here somewhere... ah, here it is! *boop boop beep* And the answer is... uh-oh, sorry, my calculator seems to have turned into a banana. Well, that's not very helpful, is it? Let's just say there are A LOT of ways to make these selections.
To find the number of ways a person can select four books, two CDs, and one DVD from the given options, we can use the concept of combinations.
The number of ways to select four books from ten is given by the combination formula:
C(n, r) = n! / (r! * (n-r)!)
Where:
n is the total number of books (10)
r is the number of books to be selected (4)
C(10, 4) = 10! / (4! * (10-4)!)
= 10! / (4! * 6!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 210
Similarly, the number of ways to select two CDs from twenty is:
C(20, 2) = 20! / (2! * (20-2)!)
= 20! / (2! * 18!)
= (20 * 19) / (2 * 1)
= 190
And the number of ways to select one DVD from five is:
C(5, 1) = 5! / (1! * (5-1)!)
= 5! / (1! * 4!)
= 5 / 1
= 5
To find the total number of ways, we multiply the number of ways for each category:
Total number of ways = C(10, 4) * C(20, 2) * C(5, 1)
= 210 * 190 * 5
= 199,500
Hence, there are 199,500 ways to select four books, two CDs, and one DVD from ten books, twenty CDs, and five DVDs.
To find the number of ways to select four books, two CDs, and one DVD from the given quantities, we can use the concept of combinations.
The number of ways to choose 4 books out of 10 is given by the combination formula:
C(10, 4) = 10! / (4! * (10 - 4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210
Similarly, the number of ways to choose 2 CDs out of 20 is:
C(20, 2) = 20! / (2! * (20 - 2)!) = 20! / (2! * 18!) = (20 * 19) / (2 * 1) = 190
And finally, the number of ways to choose 1 DVD out of 5 is:
C(5, 1) = 5! / (1! * (5 - 1)!) = 5! / (1! * 4!) = (5 * 4 * 3 * 2 * 1) / (1 * 4 * 3 * 2 * 1) = 5
To find the total number of ways, we can multiply the individual combinations together:
Total number of ways = C(10, 4) * C(20, 2) * C(5, 1) = 210 * 190 * 5 = 199,500
Therefore, there are 199,500 ways to select four books, two CDs, and one DVD from the given quantities.