Francie is planning a trip from City A to City D, during which she wil

Question

Francie is planning a trip from City A to City D, during which she will pass through both City B and City C. If there are two possible routes she could take from A to B, three possible routes she could take from B to C, and two possible routes she could take from C to D, how many possible routes could she take from A to D?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 36

Show Answer

Official Answer

C

(A) 6
(B) 7
(C) 12
(D) 14
(E) 36

IanStewart · Answer

If you're making a sequence of choices, and want to know how many possibilities there are in total, you just multiply the numbers of choices you have each time. Here we have 2 choices, then 3, then 2, so the total number of options is (2)(3)(2) = 12.

siddharthaggarwal · Answer

You can do the answer like this

3c1*3c1*2c1/3! = 12

we've to divide by 3! in order to avoid repetitions IMO answer choice C is the answer

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varmashreekanth · Answer

Hi,

I have taken the following approach to solve this question. Please correct me if I am wrong.

I have used the principle of counting i.e  OR  means  addition  and
  AND  means  multiplication

A -2-> B -3-> C -2-> D

From A to B there are 2 possible routes(say R1 and R2), so we can take any of the routes between the two i.e First Route(R1)  OR  Second Route(R2) = 1 + 1 = 2
From B to C there are 3 possible routes(say R3, R4, and R5), so we can take any of the routes among the three i.e First Route(R3)  OR  Second Route(R4)  OR  Third Route(R5) = 1 + 1 +1 = 3
From C to D there are 2 possible routes(say R6 and R7), so we can take any of the routes between the two i.e First Route(R6)  OR  Second Route(R7) = 1 + 1 = 2

Number of possible routes from A to D = (Number of possible routes from A to B)  AND  (Number of possible routes from B to C)  AND  (Number of possible routes from C to D)
 =  2 * 3 * 2   
 = 12

option C is the answer

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Francie is planning a trip from City A to City D, during which she wil

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