Problem 4 A group of four friends goes to a restaurant for dinner. The restaurant offers 12 different main dishes. Suppose that the group collectively orders four different dishes to share.The waiter just needs to place all four dishes in the center of the table. How many different possible orders are there for the group? Suppose that each individ

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Problem 4

A group of four friends goes to a restaurant for dinner. The restaurant offers 12 different main dishes.

Suppose that the group collectively orders four different dishes to share.The waiter just needs to place all four dishes in the center of the table. How many different possible orders are there for the group?
Suppose that each individual orders a main course. The waiter must remember who ordered which dish as part of the order. It’s possible for more than one person to order the same dish. How many different possible orders are there for the group?

How many different passwords are there that contain only digits and lower-case letters and satisfy the given restrictions?

Length is 7 and the password must contain at least one digit.
Length is 7 and the password must contain at least one digit and at leastone letter.

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