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A group of four friends goes to a restaurant for dinner. The restaurant offers 12 different main dishes. (i) 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? (ii) Suppose that each individual orders a main course. The waiter must re- member 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?

A group of four friends goes to a restaurant for dinner. The restaurant offers 12 different main dishes. (i) 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? (ii) Suppose that each individual orders a main course. The waiter must re- member 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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Discrete Mathematics
5 of 8 A group of four friends goes to a restaurant for dinner. The restaurant offers 12 different main dishes. (i) 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? (ii) Suppose that each individual orders a main course. The waiter must re- member 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? (iii) Length is 7 and the password must contain at least one digit. (iv) Length is 7 and the password must contain at least one digit and at least one letter. Pages 5 to 6 of 8 108%. O LT Ready Automatic en US. UTF-8
Transcribed Image Text:5 of 8 A group of four friends goes to a restaurant for dinner. The restaurant offers 12 different main dishes. (i) 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? (ii) Suppose that each individual orders a main course. The waiter must re- member 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? (iii) Length is 7 and the password must contain at least one digit. (iv) Length is 7 and the password must contain at least one digit and at least one letter. Pages 5 to 6 of 8 108%. O LT Ready Automatic en US. UTF-8
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