A flag is made of three horizontal strips of fabric, each of a solid color, either red, white, blue or green. If no two adjacent strips can be the same color, how many distinct flags are possible? These two flags are different.
Sorry, canot get picture, but it means that the order matters from top to bottom.
+36916 rwb
rbw
rgw
rwg
rgb
rbg
rwr
rbr
rgr
wbg
wgb
wbr
wrb
wgr
wrg
wrw
wgw
wbw
etc for the other two colors.....
9 x 4 = 36 is what I find
( I added the two stripes of same color but not NEXT to each other).....Anyone else?
+128473 Here's my best attempt
We have 4 ways to choose the "top" color
Then, 3 ways to choose the next color
Then, 2 ways to choose the "bottom" color
So......the total possible flags are 4 x 3 x 2 = 24
Another way to see this is all the possible sets we can make by permuting any 3 colors from a set of 4 colors....ordering the colors in the sets from left to right [ corresponding to top to bottom ], we have
4P3 = 24
+36916 That's what I did originally, but you can use the same color twice.....just not next to itself.....which adds 12 mre possibilities.
Wondering if it wouldn't be 4 choices for first color 3 choices for second color 3 choices for third color = 36 possibles.
