SOLUTION: 7 young girls are to be seated in a row. Calculate the number of different ways in which this can be done if 2 particular girls, Ushna and Manood, have exactly 3 of the other girls

Question 464107: 7 young girls are to be seated in a row. Calculate the number of different ways in which this can be done if 2 particular girls, Ushna and Manood, have exactly 3 of the other girls between them.
*Note: I know that the answer is this: (5C3) x (3!) x (3!) x (2!), but I can't understand how I get that. Please please explain this question in as much detail as possible as I cannot understand this topic. Please answer as soon as possible :) =) 卐
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!

To arrange them firstly find the number of ways to select 3 girls that will
between Ushna and Manood.
number of ways = 5C3
( select 3 girls out of 5 girls i.e except Ushna and Manood from total 7)
number of ways to arrange these 3 girls = 3!
number of ways to arrange ( 2 other girls + Ushna & Manood) = 3!
i.e here Ushna & Manood is single entity.

number of ways to arrange Ushna & Manood on their position = 2!
i.e only interchange of their position.

required number of ways = (5C3) x (3!) x (3!) x (2!)

If any doubt, you are welcome to get free help online: sudhanshu.cochin@gmail.com

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