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Standard XII

Mathematics

Combination with Restrictions

A committee o...

Question

A committee of $5$ men and $3$ women is to be formed out of $7$ men and $6$ women. If two particular women are not to be included together in the committee, then the number of committees formed is

420

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540

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336

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216

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Solution

The correct option is C $336$
Total ways without restriction is $=^{7} C_{5} \cdot^{6} C_{3}$
Total ways when the two particular ladies are included together is $=^{7} C_{5} \cdot^{4} C_{1}$
$∴$ The total number of committes formed is
$^{7} C_{5} \cdot^{6} C_{3} -^{7} C_{5} \cdot^{4} C_{1} = 336$

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Combination with Restrictions

Standard XII Mathematics

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A committee of 5 men and 3 women is to be formed out of 7 men and 6 women. If two particular women are not to be included together in the committee, then the number of committees formed is

The correct option is C 336Total ways without restriction is =7C5⋅6C3 Total ways when the two particular ladies are included together is =7C5⋅4C1 ∴The total number of committes formed is 7C5⋅6C3−7C5⋅4C1=336

A committee of $5$ men and $3$ women is to be formed out of $7$ men and $6$ women. If two particular women are not to be included together in the committee, then the number of committees formed is

The correct option is C $336$
Total ways without restriction is $=^{7} C_{5} \cdot^{6} C_{3}$
Total ways when the two particular ladies are included together is $=^{7} C_{5} \cdot^{4} C_{1}$
$∴$ The total number of committes formed is
$^{7} C_{5} \cdot^{6} C_{3} -^{7} C_{5} \cdot^{4} C_{1} = 336$