Three persons enter in a railwaycompartment. If there are 5 seats vacant,in how many ways they can take theses
Question
Three persons enter in a railwaycompartment. If there are 5 seats vacant,in how many ways they can take theses
Solution
The problem can be solved using the concept of permutations in combinatorics.
Step 1: Identify the total number of seats available, which is 5.
Step 2: Identify the total number of people, which is 3.
Step 3: Use the formula for permutations, which is nPr = n! / (n-r)!, where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.
Step 4: Substitute the values into the formula. So, we have 5P3 = 5! / (5-3)! = 5! / 2! = (54321) / (2*1) = 60.
Therefore, the three persons can take the 5 vacant seats in 60 different ways.
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