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  • In two separate rows of five chairs each, six men and four women are to be seated so that two particular girls are never apart and all the girls are not in the same row. In how many ways

In two separate rows of five chairs each, six men and four women are to be seated so that two particular girls are never apart and all the girls are not in the same row. In how many ways can they be seated? 

Option: 1

10\times 8!


Option: 2

10\times 4!


Option: 3

20\times 8!


Option: 4

20\times 4!


Answers (1)

best_answer

There will always be two girls together.

Therefore, we first choose a row to put these two girls in.

So, the number of ways to choose the 2 girls in 2 ways.

Girls can now choose two adjacent chairs in four different ways, and then sit in them in two different ways.

Seating options for these two girls are 2 + 4 + 2 = 16

At least one girl should be in a different row from the other two girls so that none of the girls are grouped together.

We, therefore, choose one of the two remaining girls to sit in the second row in 2 ways.

Now, in the second row, we choose one of five chairs to put the chosen girl in 2 ways.

Seating for the third girl is 2 + 5 = 10

The remaining seven can now be arranged into 7! Ways.

Hence, the total number of ways is given by,

16\times 10\times 7!=20\times 8!

Therefore, the number of ways for the seating arrangements is  20\times 8!  ways.

 

Posted by

Kuldeep Maurya

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