A group consists of 6 men and 5 women. Four people are selected to attend a conference. In how many ways can 4 people be selected from this group of​ 11? In how many ways can 4 men be selected from the 6​ men? Find the probability that the selected group will consist of all men.

Answer:A group consists of 6 men and 5 women. Four people are selected to attend a conference. Part A:11C4 =[tex]\frac{11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{4\times3\times2\times1\times7\times6\times5\times4\times3\times2\times1}[/tex]= [tex]\frac{11\times10\times9\times8}{4\times3\times2}[/tex]= 330Part B:6C4 = [tex]\frac{6\times5\times4\times3\times2\times1}{4\times3\times2\times1\times2\times1}[/tex]= 15Part C:[tex]\frac{6C4}{11C4}[/tex]The probability that the selected group will consist of all men is [tex]\frac{15}{330} =\frac{1}{22}[/tex]