SOLUTION: There are six people, six seats. What is the probability that both the youngest girl and the eldest boy (3 girls, 3 boys in total) are seated at each end? (yes, this one is easy..

Question 159379: There are six people, six seats. What is the probability that both the youngest girl and the eldest boy (3 girls, 3 boys in total) are seated at each end?
(yes, this one is easy...but the next question i don't get at all...)
.
.
.
What is the probability that exactly one of them (not at least, but exactly one of them) gets seated at the end?
Thanks for any help at all!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
There are six people, six seats. What is the probability that both the youngest girl and the eldest boy (3 girls, 3 boys in total) are seated at each end?
(yes, this one is easy...but the next question i don't get at all...)
# of ways to place the youngest and eldest as described: 2
# of ways to arrange the remaining 4: 4! 24
---------
Total # of ways to get the pattern you want: 2*24 = 48
Total # of ways to arrange the 6 with no restrictions: 6! = 720
----------
Probability of succeeding : 48/720 = 0.066667
========================================================.
.
.
What is the probability that exactly one of them (not at least, but exactly one of them) gets seated at the end?
# of ways to get one of them on the end: 2*2 = 4
# of ways to place the one not on the end: 4
# of ways to place the remaining 4: 4! = 24
Total # of ways to succeed: 4*4*24 = 96
Total # of ways to arrange the 6 with no restrictions: 72
Probability of succeeding: 96/720 = 0.133333..
Cheers,
Stan H.
------------
# of ways

RELATED QUESTIONS
From five girls and seven boys, six are chosen. What is the probability that there is... (answered by ewatrrr)

Six girls and eight boys walk into a video store at the same time. There are six sales... (answered by ewatrrr)

If the probability of any particular child of a family being a boy is 1/2. What is the... (answered by Edwin McCravy)

A family includes 3 kids. Determine the probability that: a. 3 are = 2 boys and one girl (answered by Fombitz)

there are 14 girls and 10 boys in an algebra 2 class. what is the probability of a group... (answered by Edwin McCravy)

The ratio of boy and girl in a school is 4:3. If there are 480 boys in the school. Find... (answered by Fombitz)

Assume that each child that is born is equally likely to be a boy or girl . If a family... (answered by ikleyn)

There are five boys and four girls in a club. If a president and Vice-President are to be (answered by solver91311)

In a family, there are 3 children. What is the probability that there are 2 girls and 1... (answered by Alan3354)