Probability Problem sets

Hey guys, so im having trouble with these questions I just started my mathematical and empirical reasoning course and I started this class 3 weeks late so the majority of class already covered most of these lessons and I missed out.., I was already able to answer this one:
1. A dance class consists of 22 students of which 10 are women and 12 are men. If 5 men and 5 women are to be chosen and then paired off, how many results are possible? I did 10x5 = 50, 12x5 = 60 then added them up and came up with 110 possiblities. I could be wrong but please let me know if I did this one correct, then I have 4 other problems I have no idea how to do!,

1. John, Jim, Jay, Jack and Joe have formed a band consisting of 5 instruments. If each of the boys can play all 5 instruments, how many different arrangements are possible? What if John and Jim can play all 5 instruments, but Jay, Jack, and Joe can each play only piano, drums, and guitar? For this one I think the first part is 120 different arrangements , I did 5x4x3x2x1, which gave me 120 but im sure im wrong.

2. Suppose you choose 5 cards from a standard 52-card deck (with 13 hearts, 13 spades, 13 clubs and 13 diamonds). How many different choices of cards are possible if
a. you can choose any 5 cards from the deck?
b. all 5 cards must be diamonds?
c. you must choose four kings and one queen?
d. you must choose 3 kings and no queens?
e. you must choose at least 1 king and at least 2 aces?

3. Suppose you choose 8 cards from a standard 52-card deck. How many different choices are possible if
a. exactly 7 cards must be of the same suit?
b. at least 7 cards must be of the same suit?
c. at most 4 cards can be of the same suit?

4. From 5 married couples, we want to select a group of 4 people that is not allowed to contain a married couple.
a. How many choices are there?
b. How many choices are there if the group must also consist of at least 2 men?

5. Suppose that 10 fish are caught at a lake that contains 4 distinct types of fish (say the types are A, B, C, and D).
a. how many different outcomes are possible, where an outcome specifies the numbers of caught fish of each of the 4 types? (for example, 4213 means 4 fish of type A, 2 fish of type B, 1 fish of type C, and 3 fish of type D are caught)
b. how many different outcomes are possible when 3 of the 10 fish are of type C?
c. how many when at least 2 fish are of type C?

eclipseaziz said:

1. A dance class consists of 22 students of which 10 are women and 12 are men. If 5 men and 5 women are to be chosen and then paired off, how many results are possible? I did 10x5 = 50, 12x5 = 60 then added them up and came up with 110 possiblities. I could be wrong but please let me know if I did this one correct, then I have 4 other problems I have no idea how to do!,

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You clearly did not read the forum's rules before posting.
We do not work out your problems. You try and we help.

On the first one you are completely off.
\(\displaystyle _{10}\mathcal{C}_5~\cdot~ _{12}\mathcal{P}_5 \)

Choose the five women first and put them in alphabetical order. Then match them the permutations of five men.

Look at this caculation.

Hi eclipseaziz:

Here's a link to a summary page of the forum guidelines.

Cheers :cool:

eclipseaziz said:

I started this class 3 weeks late so...I missed out...I have 4 other problems I have no idea how to do!

Click to expand...

There is simply no way to replace three weeks of classroom instruction with a simple forum posting. I have no idea why your academic advisor allow your university to take your money for this course; personally, I think this is unethical, since there is very little chance of this working out to your advantage, and any advisor should know that.

If online study isn't proving sufficiently helpful (so the various lessons you've studied online have left you still completely lost), then you might want to investigate hiring a qualified local tutor. By working with you face-to-face, being able to see your book and the copies of class notes you've gotten from fellow students, your tutor will be best placed to help you with personalized private lessons. With a lot of hard work and a little luck, you may be able to get caught up to the class in only a couple of weeks.