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A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then :(1) m + n = 68(2) m = n = 78(3) m = n = 68(4) n = m – 8 |
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Answer» Correct option (2) m = n = 78 Explanation: Given : (8 males, 5 females) Committee to be selected = 11 members m = no. of ways the committee is formed with at least 6 males. ⇒ (6M, 5F) or (7M, 4F) or (8M, 3F) = 8C6 × 5C5 + 8C7 × 5C4 + 8C8 × 5C3 = 78 n = no. of ways the committee is formed with atleast 3 female ⇒(8M, 3F) or (7M, 4F) or (6M, 5F) = 8C8 × 5C3 + 8C7 × 5C4 + 8C6 × 5C5 = 10 + 40 + 28 = 78 ⇒m = n = 78 |
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