Answer to Question #173200 in Combinatorics | Number Theory for Kim Galvez

Question

Use Polya’s four-step problem solving strategy to solve the following.

 

1. Consider the street map. Trisha wishes to walk directly from point A to point B. How many 

different routes can she take if she wants to go past Starbucks on Third Avenue?

2. A true-false quiz contains five questions. In how many ways can a student answer the 

questions if the student answers two of the questions with “false” and the other three with 

“true”?

3. Two U.S. coins have a total value of 35¢. One of the coins is not a quarter. What are the two 

coins?

4. If six people greet each other at a meeting by shaking hands with one another, how many 

handshakes will take place?

Answer 1

3.

25c and 10c

4.

$n=5+4+3+2+1=15$

2.

$n=C^2_5=\frac{5!}{2!3!}=10$

1.

From Sturbucks to point B she has 3 direct routes: Sturbucks - Third Avenue - Crest Boulevard - Point B, Sturbucks - Third Avenue - Gateway Boulevard - Fourth Avenue - Point B, Sturbucks - Third Avenue - Park Avenue - Fourth Avenue -Point B .

From point A to Sturbucks she has also 3 direct routes: Point A - First Avenue - Board Walk - Third Avenue -Sturbucks , Point A - River Walk - Second Avenue - Board Walk - Third Avenue - Sturbucks, Point A - River Walk - Third Avenue - Sturbucks

So she can take:

$3\cdot3=9$ routes