Question

Let a and b be positive whole numbers such that a>=b. Let there be a+b people in a line to buy tickets which each cost $5. Of them, "a" hold a $5 bill and "b" hold a $10 bill. The box office initially has an empty cash register. Demonstrate that the total amount of ways people can line up such that change is always available (for those paying with a $10 bill) is equal to (a?b+1)/(a+1) * (b+a)C(b). C means combination here (i.e. n choose k).

Name: let a and b be positive whole numbers such that ab let there be ab people in a line to buy tickets which each cost 5 of them a hold a 5 bill and b hold a 10 bill the box office initially has an empty
Uploaded: 2022-06-08T17:43:14-08:00
Duration: 3 min 51 s
Channel: Pratyush Raitan
Description: let a and b be positive whole numbers such that ab let there be ab people in a line to buy tickets which each cost 5 of them a hold a 5 bill and b hold a 10 bill the box office initially has an empty

          Let a and b be positive whole numbers such that a>=b. Let
there be a+b people in a line to buy tickets which each cost $5. Of
them, "a" hold a $5 bill and "b" hold a $10 bill. The box office
initially has an empty cash register. Demonstrate that the total
amount of ways people can line up such that change is always
available (for those paying with a $10 bill) is equal to
(a?b+1)/(a+1) * (b+a)C(b). C means combination here (i.e. n choose
k).

Added by Robert C.

Discrete Mathematics and its Applications

Kenneth Rosen 8th Edition

Chapter 8

Instant Answer

Solved by Expert Pratyush Raitan

06/08/2022

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Let a and b be positive whole numbers such that a>=b. Let there be a+b people in a line to buy tickets which each cost $5. Of them, "a" hold a $5 bill and "b" hold a $10 bill. The box office initially has an empty cash register. Demonstrate that the total amount of ways people can line up such that change is always available (for those paying with a $10 bill) is equal to (a?b+1)/(a+1) * (b+a)C(b). C means combination here (i.e. n choose k).