Permutations and Combinations Class 11 Notes - Chapter 7

According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 6.

What are Permutation and Combination?

When an event happens in m different ways, and another event happens in n different ways, then the total happening number of events is m x n.

Read more: Permutation and Combination

Equation of Permutation

If the permutation of a certain number is denoted by n with respect to time t and repetition is not allowed, then the equation is denoted by nPr and is given by nPr = n!/(n-r)! and

\(\begin{array}{l}0\leq r\leq n\end{array} \)
    • The fundamental principle of counting (FPC)

Let’s suppose from place A, there are m ways to reach place B and n ways to reach place C.

Then by FPC, there are many ways to go from Station A to Station C

    • The number of permutations of n different things taken r at a time, where
      \(\begin{array}{l}p_{1}\end{array} \)
      is the first kind of objects and
      \(\begin{array}{l}p_{2}\end{array} \)
      Are the second kind and son on to k, then the equation is represented by
\(\begin{array}{l}n!/p_{1}!p_{2}…p_(k)!\end{array} \)

Also Refer: NCERT Exemplar for Class 11 Maths Chapter 7

Equation of Combination

The definition can be constructed as the number of combinations of n different things taken r in once and is denoted by nCr and the combination formula is nCr = n!/r! (n-r)! where

\(\begin{array}{l}0\leq r\leq n\end{array} \)

Also Refer: NCERT Solutions for Class 11 Maths Chapter 7

Important Questions

  1. In an examination, in how many ways can a student select the questions if the question paper consists of 14 questions divided into Part I and Part II, containing 5 and 9 questions, respectively? A student is required to attempt 10 questions in all, selecting at least 2 from each part.
  2. If each selection of 4 cards has exactly one king in a deck of 52 cards. Determine the number of 4-card combinations out of them.
  3. How many such arrangements are possible if we need to seat 5 men and 4 women in a row so that the women occupy the even places?
  4. In how many ways can the excursion party be chosen for a class of 30 students if 15 are to be chosen?
  5. In how many ways can all the letters S be formed together to make the word ASSASSINATION?

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Frequently Asked Questions on CBSE Class 11 Maths Notes Chapter 7 Permutations and Combinations


Name some of the Geometric applications.

Applications of geometry to architecture include the use of projective geometry to create forced perspective, the use of conic sections in constructing domes and similar objects, the use of tessellations, and the use of symmetry.


What is the fundamental principle of counting?

The fundamental counting principle is a rule used to count the total number of possible outcomes in a situation.


What is permutation?

A permutation is an arrangement of objects in a definite order.


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