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?

Guest Nov 15, 2020

#1**+1 **

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

CPhill Nov 15, 2020