SOLUTION: If you are given 5 red flowers and 5 yellow flowers (All flowers are distinguishable) a) How many ways can you arrange 8 of these flowers in a row in a box? b) How many w

Algebra ->  Permutations -> SOLUTION: If you are given 5 red flowers and 5 yellow flowers (All flowers are distinguishable) a) How many ways can you arrange 8 of these flowers in a row in a box? b) How many w      Log On


   

Question 1017877: If you are given 5 red flowers and 5 yellow flowers
(All flowers are distinguishable)
a) How many ways can you arrange 8 of these flowers
in a row in a box?
b) How many ways can you arrange 8 of these flowers
in a row if you want the colors to alternate?
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
If you are given 5 red flowers and 5 yellow flowers
(All flowers are distinguishable)
a) How many ways can you arrange 8 of these flowers
in a row in a box?
(10 flowers Position 8) = 10P8 = 10*9*8*7*6*5*4*3 = 
1814400 ways.

b) How many ways can you arrange 8 of these flowers
in a row if you want the colors to alternate?
There are 2 color-wise ways for them to alternate:

RYRYRYRY and YRYRYRYR

For each of those 2 ways, we have 

(5 red flowers Position 4)(5 yellow flowers Position 4)
= (5P4)(5P4) ways.

Answer: 2(5P4)(5P4) = 2(120)(120) = 20800 ways.

Edwin