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1 boy and 6 girls are arranged in a row with 7 chairs marked A-G. How many seating arrangements are possible in which the boy sits on chair marked A?
- a)120
- b)720
- c)1440
- d)4320
- e)5040
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
1 boy and 6 girls are arranged in a row with 7 chairs marked A-G. How ...
Since order matters in this question (Seats B, C and D occupied with Jill, Greta and Pauline is a different seating arrangement from Seats B, C and D occupied with Greta, Pauline and Jill), we can solve it using either the Filling Spaces method or the Permutation formula.
Step 1: Understand the objective
There are 7 people in this question – 1 boy and 6 girls.
And, there are 7 chairs.
Each chair is unique, because it is marked with a different number.
Chair A is reserved for the only boy in the group. So, after seating the boy on chair A, we are left with 6 chairs (marked B-G) on which we have to seat 6 girls.
The question here wants us to find the total number of seating arrangements in which the boy sits on the chair marked A. This number will be equal to the number of ways in which the 6 girls can be arranged on the chairs marked B-G.
Thus, the objective of the question here is to find the number of ways in which 6 girls can be seated on 6 seats.
Step 2: Write the objective equation enlisting all tasks
The objective here consists of a single task: Arrange 6 girls on 6 seats
Thus, the objective equation will be:
Now, we know that
The number of ways in which 6 girls can be arranged in 6 seats = 6P6
So, the objective equation becomes:
(Number of arrangements in which the boy sits on Chair A) = 6P6
Step 3: Determine the number of ways of doing each task
In Step 3, using the Permutation Formula (nPn = n!), we get that
6P6 = 6! = 6*5*4*3*2*1 = 720
Step 4: Calculate the final answer
By putting these values in the objective equation, we get:
(Number of arrangements in which the boy sits on Chair A) = 720
Looking at the answer choices, we see that Option B is correct.
Most Upvoted Answer
1 boy and 6 girls are arranged in a row with 7 chairs marked A-G. How ...
Seating Arrangements with a Designated Seat
Concept: When a specific person is assigned to a designated seat, treat the person and seat as one unit and arrange the remaining people/seats.
Given:
- 1 boy and 6 girls
- 7 chairs marked A-G
- Boy sits on chair marked A
To find: Number of seating arrangements possible
Solution:
- Treat the boy and chair A as one unit.
- Remaining 6 people can be arranged in the remaining 6 seats in 6! ways.
- Multiply the number of ways to arrange the remaining 6 people by the number of ways to seat the boy on chair A.
- Total number of seating arrangements = 6! x 1 = 720
Answer: Option (B) 720
Concept: When a specific person is assigned to a designated seat, treat the person and seat as one unit and arrange the remaining people/seats.
Given:
- 1 boy and 6 girls
- 7 chairs marked A-G
- Boy sits on chair marked A
To find: Number of seating arrangements possible
Solution:
- Treat the boy and chair A as one unit.
- Remaining 6 people can be arranged in the remaining 6 seats in 6! ways.
- Multiply the number of ways to arrange the remaining 6 people by the number of ways to seat the boy on chair A.
- Total number of seating arrangements = 6! x 1 = 720
Answer: Option (B) 720
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1 boy and 6 girls are arranged in a row with 7 chairs marked A-G. How many seating arrangements are possible in which the boy sits on chair marked A?a)120b)720c)1440d)4320e)5040Correct answer is option 'B'. Can you explain this answer?
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