Question

Lorenzo is planting tulips in his garden, and he has 5 purple bulbs and 5 white bulbs to plant in one row. What is the probability that he randomly plants the bulbs so that all 5 purple bulbs are next to each other and all 5 white bulbs are next to each other? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Number of purple bulbs = 5

Number of white bulbs = 5

Total number of bulbs = 5 + 5 = 10

Number of ways in which he can plant 5 purple bulbs are next to each other and all 5 white bulbs are next to each other = 2

(5 purple first and then 5 white, 5 white first and then 5 purple)

Total number of ways to plant 10 plants in which 5 are purple and 5 are white = 10!/(5! x 5!)

= 252

P(he randomly plants the bulbs so that all 5 purple bulbs are next to each other and all 5 white bulbs are next to each other) = 2/252

= 1/126