Formula for Permutations and Combinations- Class 12

 

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 = r1  or r + r1  = n
5. C(n,0)+C(n,1)+C(n,2)+.........................C(n,n) = 2n

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