A committee of 11 members is to be formed from 8 males and 5 females. If m is number of ways committ

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6.Permutation and Combination

hard

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

$n = m \,-\, 8$

$m + n = 68$

$m = n = 78$

$m = n = 68$

(JEE MAIN-2019)

Solution

Since there are $8$ males and $5$ females. Out of these $13,$ if we select $11$ persons, then there will be at least $6$ males and at least $3$ females in the selection

$m = n = \left( {\frac{{13}}{{11}}} \right) = \left( {\frac{{13}}{2}} \right) = \frac{{13 \times 12}}{2} = 78$

Standard 11

Mathematics

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medium

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

Solution

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Determine $n$ if

$^{2 n} C_{3}:^{n} C_{3}=11: 1$