(vii) There are 3 men and 2 women. A ‘Gramswachaatta Abhiyan’ committee of two is to be formed
P is the event that the committee should contain at least one woman.
Q is the event that the committee should contain one man and one woman.
R is the event that there is not woman in the committee.
Sol. Let three men be denoted M1, M2 and M3 and two women be denoted as W1 and W2 a committee of two is formed in the following ways.
S = { M1M2, M1M3, M1W1, M1W2, M2M3, M2W1, M2W2, M3W1, M3W2, W1W2 }
n (S) = 10
P is the event that the committee should contain atleast one woman
P = { M1W1, M1W2, M2W1, M1W2, M3W1, M3W2, W1W2 }
∴ n (P) = 7
Q is the event that the committee should contain one man and one woman
Q = { M1W1, M1W2, M2W1, M2W2, M3W1, M2W2 }
∴ n (Q) = 6
R is the event that there is no woman in the committee
R = { M1M2, M1M3, M2M3 }
∴ n (R) = 3
Here, Q ∩ R = ϕ
∴ Q and R are mutually exclusive events
P ∩ R = ϕ and P U R = S
∴ P and R are complementary events.