12. The following diagram represents a map of city streets and avenues, which ar
ID: 3353787 • Letter: 1
Question
12. The following diagram represents a map of city streets and avenues, which are all one-w ay streets heading either south or east. Ryan and Malika need to take a taxi from home to the airport. Home Airport a) Calculate how many different routes the taxi could follow to take them from their home to the airport. Assume the taxi driver can only drive south or east. 3 marks) What is the probability that the taxi passes through intersection Z on the way? (1 mark) b) Module 6: Techniques of Counting .Explanation / Answer
a) numebr of ways to move from Home to end point of first block) =N(4 south and 7 east steps) =11!/(4!*7!)
=330
numebr of ways from end point of block 1 to airport =N(3 block south and 2 on east ) =5!/(3!*2!) =10
hence total number of ways from Home to airport =330*10 =3300
b) number of ways from Home to point Z =N( 3 point south and 3 point east )=6!/(3!*3!) =20
and from Z to end point of first block =5!/(1!*4!) =5
therfore total ways from Home to airport through Y =20*5*10 =1000
hence probability =1000/3300 =0.3030
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