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

`(1)/(126)` or 0.0079.

Step-by-step 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}=(10!)/(5!5!)`

`\text{Total ways}=(10* 9* 8* 7* 6* 5!)/(5* 4* 3* 2* 1* 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=(2)/(252)`

`Probability=(1)/(126)`

`Probability\approx 0.0079`

Therefore the required probability is
`(1)/(126)` or 0.0079.