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 a corner chair?a)120b)720c)1440d)4320e)5040Correct answer is option 'C'. Can you explain this answer?

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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 a corner chair?

a)
120
b)
720
c)
1440
d)
4320
e)
5040

Correct answer is option 'C'. Can you explain this answer?

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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.

In this question, two cases are possible:

Case 1: The boy sits on Chair A and the 6 girls are arranged on chairs B-G

Case 2: The boy sits on Chair G and the 6 girls are arranged on chairs A-F

The question here wants us to find the total number of seating arrangements in which the boy sits either on the chair A or on chair G. That is, the question wants us to find the total number of ways in which the 6 girls can be arranged either on chairs B-G or on chairs A-F. This is the objective of the question.

Step 2: Write the objective equation enlisting all tasks

The objective here consists of two tasks:

Task 1 – Arrange the 6 girls on the 6 seats marked B-G
Task 2 – Arrange the 6 girls on the 6 seats marked A-F

Next, we need to determine what sign to put in the objective equation – multiplication or addition.

Let’s look at the objective statement again:

“. . . to find the total number of ways in which the 6 girls can be arranged either on chairs B-G or on chairs A-F”

The objective statement contains the words ‘Either. . . Or’

This means that we will put an addition sign between the number of ways of doing the two tasks.

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 chirs A or G) = 6P₆+ 6P₆

That is,

(Number of arrangements in which the boy sits on chirs A or G) = 2 (6P₆)

Step 3: Determine the number of ways of doing each task

In Step 3, using the Permutation Formula (ⁿP_n = 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 chirs A or G) = 2 x720 = 1440

Looking at the answer choices, we see that Option C is correct.

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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 a corner chair?a)120b)720c)1440d)4320e)5040Correct answer is option 'C'. Can you explain this answer?

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