Answer

Verified

460.2k+ views

Hint- The total number of corner seats in a railway compartment are four, two on either side of the compartment.

6 boys and 4 girls enter a railway compartment having 5 seats on each side.

$ \Rightarrow $Total seats$ = 10$

$ \Rightarrow $Total number of corner seats $ = 4$(2 on either side)

$ \Rightarrow $Remaining seats$ = 10 - 4 = 6$

Hence 4 girls can occupy the 4 corner seats in 4! Ways.

Remaining 6 seats can be occupied by 6 boys in 6! Ways.

$ \Rightarrow $Total number of ways for occupying the seats if girls occupy only corner seats

${\text{ = 4!}} \times {\text{6! = }}\left( {4 \times 3 \times 2 \times 1} \right)\left( {6 \times 5 \times 4 \times 3 \times 2 \times 1} \right) = 17280$

So, 17280 is the required total number of ways for occupying the seats if girls occupy only corner seats.

So, this is the required answer.

Note- In such types of questions first calculate the number of ways of sitting boys and girls respectively such that girls occupy only corner seats then multiply the number of ways of sitting boys and girls, we will get the required number of ways of sitting such that girls occupy only corner seats.

6 boys and 4 girls enter a railway compartment having 5 seats on each side.

$ \Rightarrow $Total seats$ = 10$

$ \Rightarrow $Total number of corner seats $ = 4$(2 on either side)

$ \Rightarrow $Remaining seats$ = 10 - 4 = 6$

Hence 4 girls can occupy the 4 corner seats in 4! Ways.

Remaining 6 seats can be occupied by 6 boys in 6! Ways.

$ \Rightarrow $Total number of ways for occupying the seats if girls occupy only corner seats

${\text{ = 4!}} \times {\text{6! = }}\left( {4 \times 3 \times 2 \times 1} \right)\left( {6 \times 5 \times 4 \times 3 \times 2 \times 1} \right) = 17280$

So, 17280 is the required total number of ways for occupying the seats if girls occupy only corner seats.

So, this is the required answer.

Note- In such types of questions first calculate the number of ways of sitting boys and girls respectively such that girls occupy only corner seats then multiply the number of ways of sitting boys and girls, we will get the required number of ways of sitting such that girls occupy only corner seats.

Recently Updated Pages

What number is 20 of 400 class 8 maths CBSE

Which one of the following numbers is completely divisible class 8 maths CBSE

What number is 78 of 50 A 32 B 35 C 36 D 39 E 41 class 8 maths CBSE

How many integers are there between 10 and 2 and how class 8 maths CBSE

The 3 is what percent of 12 class 8 maths CBSE

Find the circumference of the circle having radius class 8 maths CBSE

Trending doubts

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

10 examples of law on inertia in our daily life

Write a letter to the principal requesting him to grant class 10 english CBSE

In 1946 the Interim Government was formed under a Sardar class 11 sst CBSE

Change the following sentences into negative and interrogative class 10 english CBSE