SOLUTION: Deepa's house is 5 blocks west and 4 blocks south of a bus stop. A store is 3 blocks west and 1 block south of the bus stop. How many ways can Deepa walk home if she wishes to stop

Question 1177669: Deepa's house is 5 blocks west and 4 blocks south of a bus stop. A store is 3 blocks west and 1 block south of the bus stop. How many ways can Deepa walk home if she wishes to stop at the store on her way home by walking only west and south? Please show step by step.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Represent walking one block west with W and one block south with S.

From the bus stop to the store is 3 blocks west and 1 block south. The number of different ways she can do that is the number of different ways of ordering the letters WWWS. By a well-known counting principle, the number of ways she can do that is

From the store to her house is another 2 blocks west and another 3 blocks south of the store. The number of ways she can make that part of the trip is the number of ways of ordering the letters WWSSS, which is

The fundamental counting principle then says the total number of ways she can stop at the store on the way from the bus stop to her house is 4*10 = 40.

ANSWER: 40

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