Permutations and Combinations Class 11 Notes - Chapter 7

What are Permutation and Combination?

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

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 \(P_{r}^{n}\)and is given by \(P_{r}^{n}=n!/(n-r)!\) and \(0\leq r\leq n\)

  • The fundamental principle of counting (FPC)
  • Let’s suppose from place A, there are m ways to reach a 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 \(p_{1}\) is the first kind of objects and \(p_{2}\)Are the second kind and son on to k then the equation is represented by
  • \(n!/p_{1}!p_{2}…p_(k)!\)

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 \(C_{r}^{n}\) and the combination formula is \(C_{r}^{n}=n!/r!(n-r)!\) where \(0\leq r\leq n\)

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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Practise This Question

”Each of Rajat's students either scored distinction in chemistry or physics” is represented by which of the following expressions

X : set of Rajat's students

P : x scored distinction in chemistry

Q : x scored distinction in physics