# Permutations and Combinations

• May 12th 2008, 09:21 AM
gtzfynestbabiigurl
Permutations and Combinations
1. I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected?
2. I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls?
3. State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery?
4. A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses.
How many ways can 4 toppings be selected where:

a. All the toppings are vegetables
b. All the toppings are meat
c. There is only cheese on the pizza
d. There are 2 vegetables, 1 meat and 1 cheese
e. There are 3 meats and 1 cheese.
• May 12th 2008, 11:07 AM
Soroban
Hello, gtzfynestbabiigurl!

Quote:

1) I am going to choose 6 students out of 15 to be mentors.
How many ways can a group 6 be selected?

There are: . $_{15}C_6 \:=\:{15\choose6} \;=\;5,005$ ways.

Quote:

2) I've decided that the mentor group should be made up of 3 girls and 3 boys.
Of the 15 students, 9 are girls and 6 are boys.
How many ways can I form the group

There are: . $\left(_9C_3\right)\left(_6C_3\right) \;=\;{9\choose3}{6\choose3} \;=\;1,680$ ways.

Quote:

3) State and multi-state lotteries are common in the U.S.
To win a typical lottery, you must match 6 numbers between 1 and 40.
How many different combinations are possible?

There are: . $_{40}C_6 \:=\:{40\choose6} \:=\:3,838,380$ possible combinations.

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What does that say about the chances of winning the lottery?
A lottery is a penalty for being weak in mathematics.

Quote:

1) A pizza shop offers the following toppings:
8 different vegetables, 5 different meats, and 4 different cheeses.
How many ways can 4 toppings be selected where:

a) All the toppings are vegetables.

There are: . ${8\choose3} \:=\:{8\choose4} \:=\:70$ ways.

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b) All the toppings are meat.
There are: . ${5\choose4} \:=\:5$ ways.

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c) All the toppings are cheese.
There is: . ${4\choose4} \:=\: 1$ way.

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d) There are 2 vegetables, 1 meat and 1 cheese.
There are: . ${8\choose2}{5\choose1}{4\choose1} \:=\:560$ ways.

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e) There are 3 meats and 1 cheese.
There are: . ${5\choose3}{4\choose1} \:=\:40$ ways.

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