SOLUTION: 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 de

Question 153447: 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:
All the toppings are vegetables
All the toppings are meat
There is only cheese on the pizza
There are 2 vegetables, 1 meat and 1 cheese
There are 3 meats and 1 cheese.
What's your favorite combo?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
15C6 = 15!/(16-6)!6! = [15*14*13*12*11*!0] / [1*2*3*4*5*6] = 5005
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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?
9C3 * 6C3 = 84 * 20 = 1680
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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?
40C6 = 3,838,380
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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:

All the toppings are vegetables 8C4 = 70
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All the toppings are meat 5C4 = 5
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There is only cheese on the pizza 4C4 = 1
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There are 2 vegetables, 1 meat and 1 cheese
8C2 * 5C1 * 4C1 = 28 * 5 * 4 = 560
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There are 3 meats and 1 cheese.
5C3 * 4C1 = 10*4 = 40
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What's your favorite combo?
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Cheers,
Stan H.

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