Answer:
[tex]\frac{1}{126}[/tex] 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
[tex]\text{Total ways}=\frac{10!}{5!5!}[/tex]
[tex]\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!}[/tex]
Cancel out common factors.
[tex]\text{Total ways}=252[/tex]
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
[tex]\text{Required outcomes}=2[/tex]
Formula for probability:
[tex]Probability=\frac{\text{Required outcomes}}{\text{Total ways}}[/tex]
[tex]Probability=\frac{2}{252}[/tex]
[tex]Probability=\frac{1}{126}[/tex]
[tex]Probability\approx 0.0079[/tex]
Therefore the required probability is [tex]\frac{1}{126}[/tex] or 0.0079.
