Q1 of 64 Page 122

Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.

Formula:-


nPr


Given: -


W1 can take chairs marked 1 to 4 in 4 different way.



W2 can 3 chairs from marked 1 to 4 in 3 different ways.


So, total no of ways in which women can take seat


4P2



4P2


=12


There will be 6 chairs remains



M1 take seat in any of the 6 chairs in 6 different ways,


M2 can take seat in any of the remaining 5 chairs in 5 different ways


M3 can take seat in any of the remaining 4 chairs in 4 different ways.


So, total no of ways in which men can take seat


6P3


=120


Hence total number of ways in which men and women can be seated


4P2x6P3


=1440


More from this chapter

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2

If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary. Then what is the rank of the word RACHIT?

[Hint: In each case number of words beginning with A, C, H, I is 5!]

 3

A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

 4

Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point.

[Hint: Number of straight lines =18C2 – 5C2 + 1]

 5

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