Permutations and Combinations – CBSE Class 11 Maths Solutions

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Permutations and Combinations CBSE Class 11
Maths Solutions
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Permutations and Combinations CBSE Class 11
Maths Solutions

• Permutations The numbers of arrangements
  possible of a given word or anything by taking
  some or all at a time are called permutations
  possible of that word or thing.
• Example All permutations (or arrangements)
  made with the letters x, y, z by taking two at a
  time are (xy, yx, xz, zx, yz, zy).
• Numbers of permutations of n different things,
  taken r at a time is given by
• nPr  n(n-1)(n-2). . .. . . (n-r1)
• n! / (n-r)!
• Note If there are in total n objects of which p1
  are alike of one kind p2 are alike of another
  kind p3 are alike of the third kind and so on
  and pr are alike of rth kind, such that (p1p2.
  . . . . . . . pr) n
• Then, a number of permutations possible of these
  n objects are defined as
• n! / (p1!).(p2!). . . . .(pr!)

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Permutations and Combinations CBSE Class 11
Maths Solutions

• Practice numerical problems on Permutation,
  click Class 11th Maths to know more.
• Combinations Each of the different combinations
  possible which can be formed by taking some or
  all of a number of objects is called a
  combination.
• Example Suppose we want to select two out of
  three boys X, Y, Z then,
• Possible combinations are XY, YZ ZX.
• Please note that XY and YX represent the same
  combination here.
• A number of Combinations possible of n different
  things taken r at a time is given by
• nCr  n! / (r!) (n-r)!
• Note nCn  1 and nC0 1
• nCr  nC(n-r)
•  
• Factorial Notation Let n be any positive
  integer. Then, factorial n denoted by n! is
  defined as
• n! n (n-1) (n-2). . . . . . . .3.2.1
• Eg 5! (5 4 3 2 1)
• 120
•  0! 1

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Permutations and Combinations CBSE Class 11
Maths Solutions

• Let us understand the concept of permutations
  combinations with the help of some examples
• 1. Example Evaluate 30!/28!
• Sol 30!/28! 30 29 (28!) / (28!)
• 30 29 870
• 2. Example How many 4-letter words with or
  without meaning can be formed from the letters of
  the word LOGARITHMS if repetition of the
  letters is not allowed.
• Sol As LOGARITHMS contains 10 different
  letters
• So, Number of permutations possible Number of
  arrangements possible by 10different letters
  taking4 at a time
• 10P4
• 10 9 8 7
• 5040
• 3. Example Find the value of      
  (i) 100C98        (ii) 50C 50
• Sol (i) 100C98  100C(100-98)
• 100 99 / 2 1
•  4950
• (ii) 50C50  1
• 4. Example In how many ways can a cricket team
  of eleven players be selected out from a batch of
  15 players?
• Sol Required number of ways
•  15C 11  15C (15-11)  15C 4
•  15C4  15 14 13 12 / 4 3 2 1

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Permutations and Combinations CBSE Class 11
Maths Solutions

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