Solve the following questions. These questions focus on different aspects of combinations, including calculating combinations, understanding their applications, and recognizing related concepts. I'll assume you're familiar with the basic formula for combinations: nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items chosen.
1. How many ways can you choose a committee of 4 people from a group of 11?
2. A pizza place offers 6 toppings. How many different 3-topping pizzas can you order?
3. A deck of cards has 52 cards. How many 7-card hands are possible?
4. You have 8 books. How many ways can you arrange 4 of them on a shelf?
5. A Mega Lotto has 45 numbers. You choose 6. How many different combinations are possible?
6. What is the difference between a combination and a permutation?
7. A teacher has 21 students. They need to choose 6 students to represent the class at a competition. How many different teams are possible?
8. You have 13 colored pencils. How many ways can you choose 5 to use for a drawing?
9. A basketball team has 16 players. How many ways can the coach choose a starting lineup of 5 players? (Assume all positions are equivalent.)
10. Explain why the number of combinations of choosing 3 items from a set of 6 is the same as the number of combinations of choosing 4 items from that same set of 6.
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