In a high school, a committee has to be formed form a group of $$6$$ boys $$M1$$,$$M2$$,$$M3$$,$$M4$$,$$M5$$,$$M6$$ and $$5girls$$ $$G1$$,$$G2$$,$$G3$$,$$G4$$,$$G5i)$$ Let α$$1be$$ the total number of ways in which the committee can be formed such that the committee has $$5$$ members, having exactly $$3$$ boys and $$2$$ $$girlsii)$$ Let α$$2$$ 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 $$girlsiii)$$ Let α$$3$$ be the number of ways in which the committee can be formed such that the committee has $$5$$ numbers, at least $$2$$ of them being $$girlsiv)$$ Let α$$4$$ be the total number of ways in which the committee can be formed such that the committee has $$4$$ members, having at lest $$2$$ girls and such that both and are NOT in the committee together. $$LIST-I$$ $$LIST-II$$ P. The value of α$$1$$ is $$1.136$$ Q. The value of α$$2$$ is $$2$$. $$189$$ R. The value of α$$3$$ is $$3$$. $$192$$ S. The value of α$$4$$ is $$4$$. $$200$$ $$5$$. $$381$$ $$6$$. $$461$$

Question

In a high school, a committee has to be formed form a group of $$6$$ boys $$M1$$,$$M2$$,$$M3$$,$$M4$$,$$M5$$,$$M6$$  and $$5girls$$ $$G1$$,$$G2$$,$$G3$$,$$G4$$,$$G5i)$$ Let α$$1be$$ the total number of ways in which the committee can be formed such that the committee has $$5$$ members, having exactly $$3$$ boys and $$2$$ $$girlsii)$$ Let α$$2$$ 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 $$girlsiii)$$ Let α$$3$$ be the number of ways in which the committee can be formed such that the committee has $$5$$ numbers, at least $$2$$ of them being $$girlsiv)$$ Let α$$4$$  be the total number of ways in which the committee can be formed such that the committee has $$4$$ members, having at lest $$2$$ girls and such that both and are NOT in the committee together.            $$LIST-I$$                                                                                      $$LIST-II$$            P. The value of α$$1$$  is                                                               $$1.136$$            Q. The value of α$$2$$ is                                                               $$2$$. $$189$$            R. The value of α$$3$$ is                                                               $$3$$. $$192$$                                     S. The value of α$$4$$ is                                                              $$4$$. $$200$$                                                                                                          $$5$$. $$381$$                                                                                                          $$6$$. $$461$$

Infinity Learn · Accepted Answer

(1) α$$1=6352=200$$ So P→$$4$$ (2) α$$2=6151+6252+6353+6454+6555=115$$−$$1=46$$!  So Q→$$6$$ (3) α$$3=5263+5362+5461+5560=115$$−$$5065$$−$$5164=381$$  So R→$$5$$ (4) α$$2=5262$$−$$4151+5361$$−$$4211+54=189$$ So S→$$2$$

Detailed Solution

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