Acity council consists of six democrats and five republicans. if a committee of seven people is selected, find the probability of selecting four democrats and three republicans.

Use hypergeometric distribution where there are two categories of identical objects/persons, each with a know size.
d=number of Democrats selected
D=total number of Democrats = 6
r=number of Republicans
R=total number of Republicans =5
Then 

where 
  = combination of r items selected from n,
D+R=total number of members = 6+5 =11
d+r=number of members selected = 7







the probability of selecting 4 Democrats and 3 Republicans is 5/11

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