# Thread: Probability Questions

1. ## Probability Questions

I'm having trouble with a few probability questions, any help would be great.

1. A committee is to be struck to look into the problem of overloading students with too much homework. The committee is to consist of five people selected randomly from a group of six teachers and nine students.

I've done parts a-d but I can't get part e.

e) If the entire group of eligible people is lined up randomly for a photograph before the committee selection is made, what is the probability that all the teachers are together and all the studetns are together. And what is the probability that they end up in ascending or descending ages?

2. The Aces and Kings are removed from a standard deck of playing cards and then the following little game is played. Pick a card from the well-shuffled, reduced deck and then roll a pair of dice.
Find the probability that:

a) the face value of the selected card matches that of the sum obtained on the dice (assume that Jacks and Queens have values of 11 and 12 respectively.)
b) the card value is 10 or the dice value is 10. Are the events here mutually excluive? Independent? Briefly Explain.

2. e) If the entire group of eligible people is lined up randomly for a photograph before the committee selection is made, what is the probability that all the teachers are together and all the studetns are together
You can bundle all the students and all the teachers together and count the arrangements.

TTTTTTSSSSSSSSS

There are 2 ways to arrange the bundles and 6! ways to arrange the teachers and 9! ways to arrange the students

$2\cdot{6!}\cdot{9!}$

There are 15! ways to arrange all of them.

Probability they are lined up in their respective groups:

$\frac{2\cdot{6!}\cdot{9!}}{15!}$