Answer to Question #106561 in Combinatorics | Number Theory for brady

Question

There are five different routes from Tanya's house to the mall and eight routes from the mall to the water park. How many routes are there from Tanya's house to the water park?

Answer 1

According to Fundamental principal of counting ,we known that

If a operation can be performed in $m$ ways ,and if corresponding to each of the $m$ ways of performing this operation,there are $n$ ways of performing a second operation, then the number of ways of performing the two operations together is $m×n$ .

Here, there are 5 different routes from Tanay house to mall.

And 8 routes from mall to water park.

Clearly, corresponding to each of the 5 different routes from Tanay house to mall there are 8 routes from mall to water park.

Therefore , the total number of routes from Tanay's house to water park$=5×8=40$ .