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Standard XII

Mathematics

Combination with Restrictions

From a group ...

Question

From a group of $7$ men and $6$ women five persons are to be selected to form a committee so that at least three men are there in the committee.In how many ways can it be done?

624

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702

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756

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812

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Solution

The correct option is C $756$
There are $3$ conditions
1. 3 men and 2 women
2. 4 men and 1 woman
3. 5 women
Total no of ways $=^{7} C_{3} \times^{6} C_{2}$ + $^{7} C_{4} \times^{6} C_{1}$ + $^{7} C_{5}$ $= 756$

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From a group of 7 men and 6 women five persons are to be selected to form a committee so that at least three men are there in the committee.In how many ways can it be done?

The correct option is C 756There are 3 conditions 1. 3 men and 2 women2. 4 men and 1 woman3. 5 womenTotal no of ways =7C3×6C2+ 7C4×6C1 +7C5=756

From a group of $7$ men and $6$ women five persons are to be selected to form a committee so that at least three men are there in the committee.In how many ways can it be done?

The correct option is C $756$
There are $3$ conditions
1. 3 men and 2 women
2. 4 men and 1 woman
3. 5 women
Total no of ways $=^{7} C_{3} \times^{6} C_{2}$ + $^{7} C_{4} \times^{6} C_{1}$ + $^{7} C_{5}$ $= 756$