Question

If you have 4 red tiles, 2 blue tiles and 5 purple tiles, and you randomly lay them out in a row, what is the probability that:
a. all 4 red tiles are together?
b. that all 2 blue tiles are?
c. that each of the colors is grouped together?

Answer 1

given

Red Tiles = P(R) = 4

P(B) = 2; P(P) = 5

total tiles = P(T) = 11

a) all red tiles are together

means {4 red tiles - - - -}{ remaining 7 tiles - - - - - - - }

so total spaces are = 8

so 8 ways and 4 will arrange themselves in 4! ways.

= 8! 4! / 11!

b) {2 tiles are blue _ _} { - - - - - - - - - } remaing 9 tiles

so total space is = 10

= 10! 2! / 11!

c) each colors is grouped together  

total spaces are 3! ways

so probability is = 3! 4! 2! 5! / (11!).

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