Permutations and Combinations
In a high school, a committee has to be formed from a group of $$6$$ boys $$M_{1}, M_{2}, M_{3}, M_{4}, M_{5}, M_{6}$$ and $$5$$ girls $$G_{1}, G_{2}, G_{3}, G_{4}, G_{5}$$.
(i) Let $$\alpha_{1}$$ be the total number of ways in which the committee can be formed such that the committee has $$5$$ members, having exactly $$3$$ boys and $$2$$ girls.
(ii) Let $$\alpha_{2}$$ be the total number of ways in which the committee can be formed such that the committee has at least $$2$$ members, and having an equal number of boys and girls.
(iii) Let $$\alpha_{3}$$ be the total number of ways in which the committee can be formed such that the committee has $$5$$ members, at least $$2$$ of them being girls.
(iv) Let $$\alpha_{4}$$ be the total number of ways in which the committee can be formed such that the committee has $$4$$ members, having at least $$2$$ girls and such that both $$M_{1}$$ and $$G_{1}$$ are NOT in the committee together.
LIST - I LIST - II
P. The value of $$\alpha_{1}$$ is $$1. 136$$
Q. The value of $$\alpha_{2}$$ is $$2. 189$$
R. The value of $$\alpha_{3}$$ is $$3. 192$$
S. The value of $$\alpha_{4}$$ is $$4. 200$$
$$5. 381$$
$$6. 461$$
The correct option is
Permutations and Combinations
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Permutations and Combinations
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Permutations and Combinations
(a) A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be done if at least five women have to be included in a committee? In how many of these committees (i) the women are in majority (ii) the' men are in majority?
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p = number of such committees which include at least one lady.
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Find the ratio p:q.
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Permutations and Combinations
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Permutations and Combinations
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Permutations and Combinations
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