Answer :
Answer:
The probability that the buttons for 3 consecutive floors are pressed is [tex]\frac{1}{12}[/tex] or 0.0833
Step-by-step explanation:
Consider the provided information.
They are equally likely to want to go to floors 2 through 10.
That means the number of buttons are 9.
Each presses the button for their desired floor (unless one of the others has already pressed that button).
It means that if two people wants to go at the same floors, then only one person will press the button.
Therefore, the total number of ways are: 9×8×7=504
Three consecutive floors means they have been picked:
2,3,4 or 3,4,5 or 4,5,6 or 5,6,7 or 6,7,8 or 7,8,9 or 8,9,10
We have 3 persons that means we can arrange them in 3! ways.
Therefore, the total number of favorable outcomes for this case is 7×3!=42
[tex]Probability = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}[/tex]
[tex]Probability = \frac{42}{504}=\frac{1}{12}[/tex]
Hence, the probability that the buttons for 3 consecutive floors are pressed is [tex]\frac{1}{12}[/tex] or 0.0833