Question

You are given the task to plant zo tulips in a row in front of your house. If there are 2 white, 4 pink, 4 red, and 10 yellow tulips, in how many ways. can you plant them so that no two tulips of the same color are next to each other?

Answer 1

Answer. there are 20 tulips, in a row.. Let st, t₂, tz, . - - to} to plant 2 - white ar 4- pink UP 4 - red 4R 10-yellow tulips. Joy such that no two wolours are adjacent only way to plant (yellow tulips te as follows in 20 positions. is to plant them alternately orth otherwise they'll be adjacent. there are two ways to plant 10 yellow altermately. int,=Y t3=Y, .... se tent=Y. 27 ta=r ty=Y, . . -- ge tan-Y. In remaining 10 positions ar, 4p, UR can be placed in any way because no, same color can be adjacent since, between any two colors (in remaining) 1o positions there is yellow color. or - -x2x1 ways of there are lo! = 10x 9x8x placing to plants. 7 there are 2x101 ways of placing ao plants. Answer. 2x10l = 2x (10x 9x8x .- 2x1). - 2 x 3,628,800 = 7, 257, 600