How many ways can a person select four books, two CDs, and one DVD from ten books, twenty
CDs, and five DVDs?
A)8,000
B)199,500
C)405
D)6,724,520

Question

Quizplus · Accepted Answer

We can use the formula for combinations with repetition: nCr = (n+r-1)Cr, where n is the number of items and r is the number of items to choose. Using this formula, we get:

10C4 * 20C2 * 5C1
= (10+4-1)C4 * (20+2-1)C2 * (5+1-1)C1
= 13C4 * 21C2 * 5C1
= 715 * 210 * 5
= 199,500

Therefore, there are 199,500 ways to select four books, two CDs, and one DVD from the given options. The number of ways to choose four books from ten is 10 choose 4, or 210. The number of ways to choose two CDs from twenty is 20 choose 2, or 190. The number of ways to choose one DVD from five is 5 choose 1, or 5. Using the multiplication principle, the total number of ways to choose the items is 210 x 190 x 5 = 199,500.

How Many Ways Can a Person Select Four Books, Two