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 |
||

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

Column 1 | Column 2 | Column 3 | |||

I | How many four -letter words can be formed using the letters of the word ' INEFFECTIVE ' |
(i) | 3 alike letters and 1 distinct letter | (P) | 1680 |

II | How many words can be formed by taking 4 letters at a time out of the letters of word ' MATHEMATICS ' | (ii) | 2 alike letters and 2 distinct letters | (Q) | 756 |

III | How many words can be formed by taking 4 letters at a time out of the letters of word ' EXAMINATION ' | (iii) | All different letters | (R) | 18 |

IV | How many four -letter words can be formed using the letters of the word ' INDEPENDENT ' |
(iv) | 2 alike letters of one kind and 2 alike letters of second kind | (S) | 24 |

Which of the following is the only CORRECT combination ?

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JEE Advanced 0

Column 1 | Column 2 | Column 3 | |||

I | How many four -letter words can be formed using the letters of the word ' INEFFECTIVE ' |
(i) | 3 alike letters and 1 distinct letter | (P) | 1680 |

II | How many words can be formed by taking 4 letters at a time out of the letters of word ' MATHEMATICS ' | (ii) | 2 alike letters and 2 distinct letters | (Q) | 756 |

III | How many words can be formed by taking 4 letters at a time out of the letters of word ' EXAMINATION ' | (iii) | All different letters | (R) | 18 |

IV | How many four -letter words can be formed using the letters of the word ' INDEPENDENT ' |
(iv) | 2 alike letters of one kind and 2 alike letters of second kind | (S) | 24 |

Which of the following is the only CORRECT combination ?

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JEE Advanced 0

Column 1 | Column 2 | Column 3 | |||

I | How many words can be formed by taking 4 letters at a time out of the letters of word ' INEFFECTIVE ' |
(i) | 3 alike letters and 1 distinct letter | (P) | 1680 |

II | How many words can be formed by taking 4 letters at a time out of the letters of word ' MATHEMATICS ' | (ii) | 2 alike letters and 2 distinct letters | (Q) | 756 |

III | How many words can be formed by taking 4 letters at a time out of the letters of word ' EXAMINATION ' | (iii) | All different letters | (R) | 18 |

IV | How many words can be formed by taking 4 letters at a time out of the letters of word ' INDEPENDENT ' | (iv) | 2 alike letters of one kind and 2 alike letters of second kind | (S) | 24 |

Which of the following is the only INCORRECT combination ?

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JEE Advanced 0