Write the word or phrase that best completes each statement or answers the question.
-How many different vertical arrangements are there of 9 flags if 4 are white, 3 are blue, and 2 are red?
A)1260
B)24
C)26
D)126

Question

Quizplus · Accepted Answer

To find the number of arrangements, we can use the formula for permutations with repetition:
n!/n1!n2!...nk!
where n is the total number of objects and n1, n2, ..., nk are the number of objects of each distinct type. In this case, we have:
n = 9, n1 = 4 (white flags), n2 = 3 (blue flags), and n3 = 2 (red flags)
Plugging these values into the formula, we get:
9!/4!3!2! = 1260
Therefore, the answer is choice A, 1260. This is a permutation problem, where order matters. Using the formula for permutations of n objects taken r at a time, we get:

P(9,4) * P(5,3) * P(2,2)

= (9!/(9-4)!) * (5!/(5-3)!) * (2!/(2-2)!)

= 1260. Therefore, there are 1260 different vertical arrangements possible.

Write the Word or Phrase That Best Completes Each Statement