Permutations and Probability

Evan93

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May 3, 2006
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Word Problems- Please show me how you solved them. Or explain in detail.

Lucinda has onions, tomatoes, cabbage, potatoes, carrots, celery, and peas. She uses 4 of the vegetables in a stew. How many combinations of 4 vegetables can be made with 7 vegetables?

AND...
There are 5 emtpy seats in the cafe. Monya and 6 friends awant to eat there. How many combinations of 5 students can be made from 7 students. Thank you.
 
Evan93 said:
Word Problems- Please show me how you solved them. Or explain in detail.

Lucinda has onions, tomatoes, cabbage, potatoes, carrots, celery, and peas. She uses 4 of the vegetables in a stew. How many combinations of 4 vegetables can be made with 7 vegetables?

AND...
There are 5 emtpy seats in the cafe. Monya and 6 friends awant to eat there. How many combinations of 5 students can be made from 7 students. Thank you.

For the first problem, it doesn't make any difference what order you add the vegetables....so, you are looking for a combination of 7 things taken 4 at a time.

There is a formula for this:

n C r = (r!) / (n!)(r - n)!

7 C 4 = (7!) / (4!)(7 - 4)!
or,
7 C 4 = (7 * 6 * 5 * 4!) / (4!)(3*2*1)

The 4!'s cancel out, leaving
7*6*5
----------
3*2*1

You can do some more canceling....and then do the arithmetic to get 7*5, or 35 possible combinations.

The second problem is similar. You have 7 students, and you need a group of 5 to sit in the 5 chairs. It doesn't make any difference what order the students sit in, so this is a combination of 7 things taken 5 at a time.

7 C 5 = (7!) / (5!)(7 - 5)!
or,
7 C 5 = (7!) / (5!) (2!)

7*6*5!
--------
5! * 2*1

7*6
-----
2*1

You can finish the arithmetic.

I hope this helps you.
 
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