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A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?5
Q: A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?
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Answer : 3. "246"
Explanation :
Answer: C) 246 Explanation: A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking. (i) 1 lady out of 4 and 4 gentlemen out of 6 (ii) 2 ladies out of 4 and 3 gentlemen out of 6 (iii) 3 ladies out of 4 and 2 gentlemen out of 6 (iv) 4 ladies out of 4 and 1 gentlemen out of 6 In case I the number of ways = C14×C46 = 4 x 15 = 60 In case II the number of ways = C24×C36 = 6 x 20 = 120 In case III the number of ways = C34×C26 = 4 x 15 = 60 In case IV the number of ways = C44×C16 = 1 x 6 = 6 Hence, the required number of ways = 60 + 120 + 60 + 6 = 246