How many ways can 6 people be seated in a row if two specific people must sit to

₹0.0

Question: How many ways can 6 people be seated in a row if two specific people must sit together?

Options:

Correct Answer: 120

Solution:

Treat the two specific people as one unit. So, we have 5 units to arrange: 5! × 2! = 120.

How many ways can 6 people be seated in a row if two specific people must sit together?

How many ways can 6 people be seated in a row if two specific people must sit together?

Step 1: Identify the two specific people who must sit together. Let's call them Person A and Person B.
Step 2: Treat Person A and Person B as one single unit or block. This means instead of 6 individual people, we now have 5 units to arrange: the block (A and B together) and the other 4 people.
Step 3: Calculate the number of ways to arrange these 5 units. The formula for arranging n units is n!. So, we calculate 5! (which is 5 factorial).
Step 4: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120.
Step 5: Now, within the block of Person A and Person B, they can switch places. This means there are 2 ways to arrange them (A next to B or B next to A).
Step 6: Multiply the number of arrangements of the 5 units by the arrangements of the block. So, we calculate 5! × 2! = 120 × 2 = 240.
Step 7: The final answer is 240. This is the total number of ways to seat the 6 people with the condition that Person A and Person B sit together.

Permutations with Restrictions – This concept involves arranging items with specific conditions, such as grouping certain items together.
Factorial Calculations – Understanding how to calculate permutations using factorials is crucial for solving arrangement problems.