SOLUTION: Seven students, including Jack and Jill, sit randomly in a row of seven chairs. What is the probability that Jill is sitting in the first chair? What is the probabilit

Algebra ->  Permutations -> SOLUTION: Seven students, including Jack and Jill, sit randomly in a row of seven chairs. What is the probability that Jill is sitting in the first chair? What is the probabilit      Log On


   

Question 1122549: Seven students, including Jack and Jill, sit randomly in a row of seven chairs.
What is the probability that Jill is sitting in the first chair?

What is the probability that Jill is sitting in the first chair and Jack is not sitting in the second chair?

Enter your answers as fractions in lowest terms.
Answer by Alex.33(110) About Me  (Show Source):
You can put this solution on YOUR website!
The number of all possibilities: 7P7=7!

The number of the cases where Jill has the first chair: 6P6(since Jill has had the first chair, the variable is just the rest 6 chairs)=6!
P(Jill in first chair)=6!/7!=1/7.

The number of the cases where Jill has the first and Jack has the second: 5P5=5!
P(Jill in first and Jack not in second)=(6!-5!)/7!=5/42.

And we're done.