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Combinations

If a coin is flipped twenty times, how many ways are there to get exactly ten tails and ten heads?

Choosing Subsets Warmup

         

2 adults and 5 children are going for a ride in a minivan with 2 front seats, 2 middle seats, and 3 back seats. If the adults sit in the front seats, how many different ways are there to choose which 2 of the 5 children sit in the middle seats?

10 people visit a buffet. The buffet has 5 dishes, and each person orders a 2-dish combo. Is it possible for each of the 10 people to choose a different pair of dishes?

How many different ways can you walk from the corner of 1st St. and 1st Ave. to the corner of 4th St. and 3rd Ave. if you only walk North and East?

How many different ways are there to tile a 2 by 8 rectangle with identical 2 by 1 dominoes so that exactly 2 of the dominoes are vertical?

2 adults and 5 children are going for a ride in a minivan with 2 front seats, 2 middle seats, and 3 back seats. If the adults sit in the front seats, how many different ways are there to choose which 3 of the 5 children sit in the back seats?

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