Four roads join Jaipur to Ajmer and three roads join Ajmer to Udaipur. Farhan drives from Jaipur to Udaipur through Ajmer and back again through Ajmer, and he does not use any road a second time. How many different round trips are possible?

12Correct answerYour answer24Correct answerYour answer72Correct answerYour answer144Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Going: $4 \times 3 = 12$ ways.
Returning: one Udaipur–Ajmer road and one Ajmer–Jaipur road are already used, so $2 \times 3 = 6$ ways.
Round trips $= 12 \times 6 = 72$ .

Worth noting

144 is $12 \times 12$ , which allows a road to be reused. 12 counts only the outward journey.

Ten questions from Counting and Basic Probability, at your own pace.

Explanation