Permutations and Combinations

In a high school, a committee has to be formed from a group of 6 boys M

(i) Let α

(ii) Let α

(iii) Let α

(iv) Let α

The correct option is:

_{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 α

_{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 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 girls.(iii) Let α

_{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 α

_{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 |
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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 |

The correct option is:

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JEE Advanced 2018

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JEE Advanced 2012

Consider all possible permutations of the letters of the word ENDEANOEL.

Match the Statements/ Expressions in Column I with the statements/ Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the matrix given in the ORS.

Column I |
Column II |
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(A) | The number of permutations containing the word ENDEA is | (p) | 5! |

(B) | The number of permutations in which the letter E occurs in the first and the last positions is | (q) | |

(C) | The number of permutations in which none of the letters D, L, N occurs in the last five positions is | (r) | |

(D) | The number of permutations in which the letters A, E, O occur only in odd positions is | (s) |

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JEE 2008