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
