How many different vertical arrangements are there of 8 flags if 4 are white, 2 are blue, and 2 are red?
A) 420
B) 20
C) 70
D) 16

Question

Quizplus · Accepted Answer

The total number of arrangements can be calculated using the formula for permutations of a multiset: $ \frac{n!}{n_1!n_2!n_3!...} $, where $ n $ is the total number of items, and $ n_1, n_2, n_3, ... $ are the counts of identical items. Here, $ n = 8 $ (total flags), $ n_1 = 4 $ (white flags), $ n_2 = 2 $ (blue flags), and $ n_3 = 2 $ (red flags). So, the total number of arrangements is $ \frac{8!}{4!2!2!} = 420 $.

How Many Different Vertical Arrangements Are There of 8 Flags