# Six boys and four girls enter a railway compartment having 5 seats on each side. In how many ways can they occupy the seats if the girls are to occupy only the corner seats?

Last updated date: 16th Mar 2023

•

Total views: 308.1k

•

Views today: 6.87k

Answer

Verified

308.1k+ 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

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

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

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE