Question

Joyce is planting tulips in her garden, and she has 5 red bulbs and 5 white bulbs to plant in one row. What is the probability that she randomly plants the bulbs so that all 5 red 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

Answer:

$\frac{1}{126}$ or 0.0079.

Explanation:

Joyce is planting tulips in her garden.

Number of red (R) bulbs = 5

Number of white (W) bulbs = 5

Total number of ways to plant 10 bulbs in one row is

$\text{Total ways}=\frac{10!}{5!5!}$

$\text{Total ways}=\frac{10\times 9\times 8\times 7\times 6\times 5!}{5\times 4\times 3\times 2\times 1\times 5!}$

Cancel out common factors.

$\text{Total ways}=252$

It is given that she randomly plants the bulbs so that all 5 red bulbs are next to each other and all 5 white bulbs are next to each other.

Required outcomes are

RRRRRWWWWW and WWWWWRRRRR

$\text{Required outcomes}=2$

Formula for probability:

$Probability=\frac{\text{Required outcomes}}{\text{Total ways}}$

$Probability=\frac{2}{252}$

$Probability=\frac{1}{126}$

$Probability\approx 0.0079$

Therefore the required probability is $\frac{1}{126}$ or 0.0079.