7. How many different ways can the letters in “COUNT” be arranged? 8. How many different...

7. How many different ways can the letters in “COUNT” be arranged? 8. How many different ways can the letters in “PROBABILITY” be arranged?

9. A pizza restaurant offers 15 different toppings, but only allows customers to select up to four different toppings for each pizza. How many different ways are there for customers to choose up to four toppings for a pizza?

10. A youth soccer team consists of 12 players. When they have games, they play simultaneously on two fields, so the team is divided into two groups of 6. How many ways can the 12 players be divided into two groups of six players if we only care which players are grouped together? Thanks!

Expert Solution

Solution: 7. How many different ways can the letters in “COUNT” be arranged?

Answer: Since there are five non repeating letters in the word "COUNT", therefore, the number of different ways is:

8. How many different ways can the letters in “PROBABILITY” be arranged?

Answer: Since there are 11 letters in the word "PROBABILITY", of which two letters "B" and "I" are repeating two times each. Therefore the number of different ways is:

9. A pizza restaurant offers 15 different toppings, but only allows customers to select up to four different toppings for each pizza. How many different ways are there for customers to choose up to four toppings for a pizza?

Answer: The different ways for customers to choose up to four toppings for a pizza is 15C4

10. A youth soccer team consists of 12 players. When they have games, they play simultaneously on two fields, so the team is divided into two groups of 6. How many ways can the 12 players be divided into two groups of six players if we only care which players are grouped together?

Answer: The number of ways 12 players can be divided into two groups of six players is:

orchestra answered 2 years ago

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