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There is a committee composed of eight women and two men. When they meet, they sit in a row---the women in distinguishable rocking chairs and the men on indistinguishable stools. How many distinct ways are there for me to arrange the ten chairs and stools for a meeting?

 Nov 15, 2020
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Consider  the set   ( A, B , C, D, E, F, G ,H , I ,J )....let A,B  be the indistinguishable  chairs and the  rest  distinguishable stools

 

We can chose any  8 of 10  places  for the distinguishable chairs to be placed and for each of these they  can be  arranged  in 8! ways.....note that once we  do  this, the indistinguishable stools don't matter because their places are "set" and the placement of A....B  looks just  like the placement of  B ....A

 

So

 

C (10,8) * 8!  =  1,814,400  arrangements

 

 

cool cool cool

 Nov 15, 2020
edited by CPhill  Nov 15, 2020

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