JEE PYQ: Permutation And Combination Question 34
Question 34 - 2019 (09 Apr Shift 1)
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) $n = m - 8$
(4) $m = n = 68$
Show Answer
Answer: (2)
Solution
$m = {}^8C_6 \cdot {}^5C_5 + {}^8C_7 \cdot {}^5C_4 + {}^8C_8 \cdot {}^5C_3 = 28 + 40 + 10 = 78$. $n = {}^5C_3 \cdot {}^8C_8 + {}^5C_4 \cdot {}^8C_7 + {}^5C_5 \cdot {}^8C_6 = 10 + 40 + 28 = 78$. So $m = n = 78$.
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