Fundamental principle of counting for path combinations
Question
A, B and C are three places such that there are three different roads from A to B, four different roads from B to C and three different roads from A to C. In how many different ways can one travel from A to C using these roads?
Options
10
13
15
36
Explanation
There are two completely independent primary routes to travel from A to C: an indirect route via B, and a direct route.
Route 1 (Indirect via B): Travel A to B (3 options) AND travel B to C (4 options). Combinations = 3 × 4 = 12 ways.
Route 2 (Direct to C): Travel A to C directly (3 options). Combinations = 3 ways.
Since the traveler must choose either Route 1 or Route 2, add the independent possibilities together: Total ways = 12 + 3 = 15 ways.
Answer: (c).
Question details
Year
2022
Paper
CSAT
Question
Q27
Section
Numerical Ability
Sub-topic
Permutations & Combinations
Type
Factual single
Difficulty
Easy
Source hint
Roads from A to B to C
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