A man has to travel from Allahabad to Lucknow and then from Lucknow to Kolkata. If there are 5 routes from Allahabad to Lucknow and 4 routes to go from Lucknow to Kolkata, then how many options are available for the man to travel from Allahabad to Kolkata via Lucknow?
Solution
Correct Answer: Option B
This problem can be solved using the M-N-P rule.
Rule – If there are three things to do and there are M ways to do the first thing, N ways to do the second thing and P ways to do the third thing then there will be M × N × P ways to do all the three things together.
Thus, to travel from Allahabad to Kolkata via Lucknow
There are M = 5 routes to travel from Allahabad to Lucknow
There are N = 4 routes to travel from Lucknow to Kolkata
Then, M × N = 5 × 4 = 20 ways to travel from Allahabad to Kolkata via Lucknow.
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