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Byju's Answer

Standard XII

Mathematics

Permutation under Restriction

From a group ...

Question

From a group of $8$ women and $6$ men, a committee of $3$ men and $3$ women is to be formed. In how many ways can the committee be formed if one man and one woman refuses to serve together?

722

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784

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610

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896

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Solution

The correct option is B $784$
$1$ man refuse to serve together say man A and Women B.
There are three conditions.
1. If man A is selected and B is not selected.
$=^{7} C_{2} \times^{5} C_{3} = 210$ (1)
2. If women B is selected and A is not selected.
$=^{7} C_{3} \times^{5} C_{2} = 350$
3. Both are not selected.
$=^{7} C_{3} \times^{5} C_{3} = 224$
Total Number of ways $= 784$

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From a group of 8 women and 6 men, a committee of 3 men and 3 women is to be formed. In how many ways can the committee be formed if one man and one woman refuses to serve together?

The correct option is B 7841 man refuse to serve together say man A and Women B.There are three conditions.1. If man A is selected and B is not selected.=7C2×5C3=210 (1)2. If women B is selected and A is not selected.=7C3×5C2=350 3. Both are not selected.=7C3×5C3=224 Total Number of ways =784

From a group of $8$ women and $6$ men, a committee of $3$ men and $3$ women is to be formed. In how many ways can the committee be formed if one man and one woman refuses to serve together?