# NCERT Class 11-Math՚S: Chapter – 7 Permutations and Combinations Part 10 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 57**:

Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is

[**Hint**: After sending 4 on one side and 3 on the other side, we have to select out of ; on one side and 6 on the other. Now there are on each side of the long table and each can be arranged in ways.]

**Answer: True**

**Question 58**:

A candidate is required to answer 7 questions out of questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in ways.

**Answer: False**

**Question 59**:

To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is .

**Answer: False**

In each if the Exercises from 60 to 64 match each item given under the column to its correct answer given under the column .

**Question 60**:

There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:

(a) | One book of each subject | (i) | |

(b) | At least one book of each subject | (ii) | |

(c) | At least one book of English | (iii) |

**Answer**

(a) ⟷ (ii)

(b) ⟷ (iii)

(c) ⟷ (i)

**Question 61**:

Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:

(a) | Boys and girls alternate | (i) | |

(b) | No two girls sit together | (ii) | |

(c) | All the girls sit together | (iii) | |

(d) | All the girls are never together | (iv) |

**Answer**:

(a) ⟷ (iii)

(b) ⟷ (i)

(c) ⟷ (iv)

(d) ⟷ (ii)

**Question 62**:

There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:

(a) | In how many ways committee can be formed | (i) | |

(b) | In how many ways a particular professor is included | (ii) | |

(c) | In how many ways a particular lecturer is included | (iii) | |

(d) | In how many ways a particular lecturer is excluded | (iv) |

**Answer**

(a) ⟷ (iv)

(b) ⟷ (iii)

(c) ⟷ (ii)

(d) ⟷ (i)

**Question 63**:

Using the digits , a number of 4 different digits is formed. Find

(a) | How many numbers are formed? | (i) | |

(b) | How many numbers are exactly divisible by 2? | (ii) | |

(c) | How many numbers are exactly divisible by 25? | (iii) | |

(d) | How many of these are exactly divisible by ? | (iv) |

**Answer**:

(a) ⟷ (i)

(b) ⟷ (iii)

(c) ⟷ (iv)

(d) ⟷ (ii)

**Question 64**:

How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

(a) | 4 letters are used at a time | (i) | |

(b) | All letters are used at a time | (ii) | |

(c) | All letters are used but the first is a vowel | (iii) |

**Answer**:

(a) ⟷ (iii)

(b) ⟷ (i)

(c) ⟷ (ii)