UPSC Prelims 2011·CSAT·Quantitative Aptitude·Combinatorics and Probability

There are four routes to travel from city A to city B and six routes from city B to city C. How many routes are possible to travel from the city A to city C?

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Last updated 23 May 2026, 3:31 pm IST
  1. A24Correct
  2. B12
  3. C10
  4. D8

Explanation

The correct answer is A) 24. Explanation: To find the total number of possible routes from city A to city C, passing through city B, we use the multiplication principle of counting. If there are 'm' ways to do one task and 'n' ways to do a second task, then there are 'm x n' ways to do both tasks in sequence. 1. Number of routes from city A to city B = 4. 2. Number of routes from city B to city C = 6. Total routes from city A to city C = (Routes A to B) x (Routes B to C) Total routes = 4 x 6 = 24. Analysis of options: A) 24: This is correct, derived from multiplying the number of routes for each segment of the journey. B) 12: Incorrect. This would be 4 x 3 or 6 x 2, not applicable here. C) 10: Incorrect. This would be 4 + 6, which is the addition principle, used when choosing one route OR another, not when performing actions in sequence. D) 8: Incorrect. This would be 4 x 2 or 6 + 2, not applicable here.
Quantitative Aptitude: There are four routes to travel from city A to city B and six routes from city B to city C. How many routes are possible
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