Three different roads connect Kochi to Thrissur, and four different roads connect Thrissur to Palakkad. In how many ways can Joseph drive from Kochi to Palakkad through Thrissur?

12Correct answerYour answer24Correct answerYour answer64Correct answerYour answer81Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The first leg can be done in 3 ways, and each of these can be followed by any of the 4 roads on the second leg.
Routes $= 3 \times 4 = 12$ .

Worth noting

24 doubles the answer as if the trip were a round trip. 64 and 81 are $4^3$ and $3^4$ : powers are for repeating the SAME choice, not for two different legs.

Concept: Counting routes in stages
Typical timeTypical: 40 s
Your timeYours: —

The rule this testsThe counting principle

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Three different roads connect Kochi to Thrissur, and four different roads connect Thrissur to Palakkad. In how many ways can Joseph drive from Kochi to Palakkad through Thrissur?

Explanation