NCERT Exemplar Solutions
Class 11 - Mathematics - Chapter 7: PERMUTATIONS AND COMBINATIONS

Short Answer Type

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.

If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary order, then what is the rank of the word RACHIT?

A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing the questions.

Out of 18 points in a plane, no three are collinear except five points which are collinear. Find the number of lines that can be formed joining the points.

We wish to select 6 persons from 8, but if the person A is chosen, then B must also be chosen. In how many ways can selections be made?

How many committees of five persons with a chairperson can be selected from 12 persons?

How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.

Find the number of permutations of \(n\) distinct things taken \(r\) together in which three particular things must occur together.

Find the number of different words that can be formed from the letters of the word TRIANGLE so that no vowels are together.

Find the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is repeated.

There are 10 persons named \(P_1, P_2, \dots, P_{10}\). Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement \(P_1\) must occur whereas \(P_4\) and \(P_5\) do not occur. Find the number of such possible arrangements.

There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.

A box contains two white, three black, and four red balls. In how many ways can three balls be drawn if at least one black ball is included?

If \(^nC_{r-1} = 36\), \(^nC_r = 84\) and \(^nC_{r+1} = 126\), then find \(r\).

Find the number of integers greater than 7000 that can be formed with digits 3, 5, 7, 8 and 9 where no digit is repeated.

If 20 lines are drawn in a plane such that no two are parallel and no three are concurrent, in how many points will they intersect?

In a certain city, telephone numbers have six digits, the first two digits being one of 41, 42, 46, 62 or 64. How many telephone numbers have all six digits distinct?

In an examination, a student has to answer 4 questions out of 5, with questions 1 and 2 being compulsory. Determine the number of ways in which the student can make the choice.

A convex polygon has 44 diagonals. Find the number of its sides.