PERMUTATIONS AND COMBINATIONS

Summary

Fundamental principle of counting If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of occurrence of the events in the given order is m × n.

The number of permutations of n different things taken r at a time, where repetition is not allowed, is denoted by nPr and is given by {^n}P_r = \frac{n!}{(n-r)!}, where 0 ≤ r ≤ n.

n! = 1 × 2 × 3 × ...×n

n! = n × (n – 1) !

The number of permutations of n different things, taken r at a time, where repetition is allowed, is nr

The number of permutations of n objects taken all at a time, where p1 objects are of first kind, p2 objects are of the second kind, ..., pk objects are of the kth kind and rest, if any, are all different is \frac{n!}{{p_1}! {p_2}! ... {p_k}!}

The number of permutations of n different things taken r at a time, where repetition is not allowed, is denoted by nCr and is given by {^n}C_r = \frac{n!}{r! (n-r)!}, where 0 ≤ r ≤ n.

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Lecture - 1

  • Fundamental Principle of Counting
  • NCERT Exercise 7.1 (Q1 to Q6)
  • Factorial of a number
  • NCERT Exercise 7.2 (Q1 to Q5)

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Lecture - 2

  • Meaning of Permutations
  • Derivation for rule of Permutations
  • NCERT Exercise 7.3 (Q1 to Q9)

Hindi + English

Lecture - 3

  • Number of Permutations when an alphabet repeat
  • NCERT Example 14 and Example 16
  • NCERT Exercise 7.3 (Q10 & Q11)

Hindi + English

Lecture - 4

  • Meaning of Combination, how combination is different from permutations, derivation of rule for combinations through permutations
  • Shortcuts and special cases of combinations
  • NCERT Exercise 7.4 (Q1 to Q9)
  • NCERT Example 19

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Lecture - 5

  • NCERT Miscellaneous Exercise (Q1 to Q11)

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