A gardener has 12 tulip bulbs to plant in a box (4 columns by 3 rows). There are 4 white, 4 red and 4 yellow bulbs, and exactly one bulb is planted in each small square.
a. How many different color patterns are possible?
b. How many of these patterns have each row entirely the same color?
c. How many of these patterns have the four corner squares the same color?
The Attempt at a Solution
a. I think this one is 12!/4!4!4!
b. and i think this one is 3!
Could I just get a confirmation of these 2?
c. Since the 4 bulbs of one color would be in the corner places, take 4 away from the original 12 spots available to get the other 2 colors' placement possibilities: 8!/4!4! I'm not sure if that's right and I think that I have to multiply something to represent the color that is in the 4 corners
Sorry I forgot to make a good title for the post...