Question 253039
A city council consists of 7 males and 4 females.
Total number of counsilors = 7+4 = 11 
Two counsilors are selected at random 
Total number of ways of forming the committee= 11C2
                                             = 11*10/2
                                             =55
A) If both counsilors are males
  Out of 7 males 2 can be selected in 7C2 ways
  Number of favourable events = 7*6/2 = 21
  Probability p(A) = 21/55
B)one councilor is a male and one a female
  Out of 7 males 1 can be selected in 7 ways and out of 4 females 1 can be selected in 4 ways.
  Number of favourable events = 7*4 = 28
  Probability p(B) = 28/55
C). At least one councilor is a female
There are two possibilities.
one male and one female or 2 females.
In the first case probability = 28/55  ...(1)
In the second case, out of 4 females 2 can be selected in 4C2 ways.
Number of favourable events = 4*3/2 = 6
  Probability  = 6/55                  ...(2)
The required probability that at least one councilor 
                      is a female = (28/55)+(6/55)
                                  = 34/55