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Find the number of ways to arrange $6$ men in a row such that $3$ particular men are consecutive.

Now first I have to select those $3$ men which can be done in $C(6,3)$ ways. How do I proceed?

Thanks

N. F. Taussig
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J. Deff
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    You don't have to choose the three particular men. They're chosen for you, which is what they phrasing means. – Arthur Apr 12 '17 at 09:57
  • @Arthur i think this is what i missed. if particular word was not written in question then how would i have proceeded? – J. Deff Apr 12 '17 at 10:11
  • Well, then the whole "consecutive" thing would be a bit strange, saying that the are three men that should be consecutive, but it doesn't matter who they are. Might as well just ask about the number of ways to arrange then without restrictions, which gives $6!=720$ ways. – Arthur Apr 12 '17 at 11:12

1 Answers1

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Initially, we can view the three particular men who sit in a block of consecutive seats as one object, which gives us four objects to arrange, the block of three men who sit in consecutive seats and the other three men. How many ways can the four objects be arranged in a row?

$4!$

How many ways can the three particular men be arranged within the block?

$3!$

How many seating arrangements does this yield?

$4!3!$

N. F. Taussig
  • 76,571