Best Website for Maths learners

Thursday, 18 July 2019

Formula for Permutations and Combinations

Permutations:

Arrangement of objects taken some or all at a time is known as Permutation.

Formula:

  1. Permutations of n different objects taken r at a time is P(n,r) = n!/(n-r)!
  2. Permutations of n objects taken all of them at a time when p of them of one kind, q of them be another kind and r of them be third kind, then the required number of permutations is = n!/(p!q!r!)
  3. The permutations of n objects taken r at a time when each object may repeat any number of times = nr
  4. Permutations of n objects arranged in circle =(n-1)!
  5. Permutations of n objects in the case of necklace or beads of bracelets=(n-1)!/2.

Combinations:

The selection of objects taken some or all of them at a time without regarded to the order is known as Combination.

Formula:

Number of combinations of n objects taken r at a time is= C(n,r) = n!/(n-r)!r!

Note:

  1. C(n,0)=C(n,n)=1
  2. C(n,r)=C(n,n-r)
  3. C(n,r)+C(n,r-1)= C(n+1,r)
  4. C(n,r)=C(n,r1) then r = r or r + r1  = n
  5. C(n,0)+C(n,1)+C(n,2)+.........................C(n,n) = 2n
For more Educational Resources go to the Edcopy.com


No comments:

Post a Comment