There are 5 routes to go from Prayagraj to Patna and 4 routes to go from Patna…
2023
There are 5 routes to go from Prayagraj to Patna and 4 routes to go from Patna to Kolkata. How many ways are possible for going from Prayagraj to Kolkata via Patna?
Answer: B. 20 — CONCEPTWhen a task is completed through successive independent stages, the multiplication principle applies: multiply the number of choices available at each…
- A.
45
- B.
20
- C.
54
- D.
More than one of the above
- E.
None of the above
Attempted by 90 students.
Show answer & explanation
Correct answer: B
CONCEPT
When a task is completed through successive independent stages, the multiplication principle applies: multiply the number of choices available at each stage. Each ordered pair of stage choices represents one complete outcome.
APPLICATION
Choose a route from Prayagraj to Patna: 5 choices.
For each first-leg choice, choose a route from Patna to Kolkata: 4 choices.
By the multiplication principle, the number of complete journeys is 5 × 4 = 20.
CROSS-CHECK
Listing four second-leg choices for each of the five first-leg choices gives 4 + 4 + 4 + 4 + 4 = 20.
Result: There are 20 possible journeys via Patna.