Question
Download Solution PDFFigure-out the number of ways can 5 women and 3 men be seated in a row so that two men are together?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
There are 5 women and 3 men.
Two particular men sit together.
Concept:
These types of questions are usually done by taking two particular men as a single unit, applying permutations within them, and then making permutations of all the units.
Formula:
Ways of arranging n distinct things taken all at a time = n!
Explanation:
Let the two particular men be M1 and M2
Number of ways of choosing and arranging the 2 men out of 3 = 3C2 × 2! = 6
Now, taking these chosen 2 men as a single unit, the number of ways of arranging 1 man, 2 men as a single unit, and 5 women taking at a time = (3- 2 +1 + 5)! = 7! = 5040
So, the number of ways can 5 women and 3 men are seated in a row so that two men are together = 3C2 × 2! × (3- 2 +1+ 5)! = 6 × 5040 = 30240
Last updated on Jun 19, 2025
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