Figure-out the number of ways can 5 women and 3 men be seated in a row so that two men are together?

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AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 1)
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  1. 7200
  2. 720
  3. 2400
  4. 30240

Answer (Detailed Solution Below)

Option 4 : 30240
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Detailed Solution

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Given:

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  = 3C× 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 =  3C× 2! × (3- 2 +1+ 5)! = 6 × 5040 = 30240

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