A committee of two persons is selected from two men and two women. What is the probability that the committee will have will have (i) no man (ii) one man (iii) two men ??

experts please do help !!

no. of ways of selecting 2 persons out of 4 = 4C_{2 }= 6

(1) No. of ways of selecting no man or 2 women = 2C_{2 }= 1

required probability = 1/6

(2)no. of ways of selecting 1 man out of 2 men = 2C_{1 }= 2

no. of ways of selecting 1 woman out of 2 women = 2C_{1 }= 2

required probability = (2*2)/6 = 4/6 = 2/3

(3) no. of ways of selecting 2 men out of 2 men = 2C_{2 }= 1

required probability = 1/6

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