## Tuesday, November 24, 2009

### GMAT/CAT PREPARATION EMAIL COURSE DAY 28

PERMUTATIONS & COMBINATIONS

COMBINATIONS

Number of selections of n different objects taken ‘r‘ at a time.

If the order doesn't matter, it is a Combination.

Number of combinations of n dissimilar things taken 'r' at a time is denoted by nCr & is given by nCr =n!/(n-r)!r!

Number of combinations of n different things taken ‘r’ at a time in which ‘p’ particular things will always occur is (n–p)C(r–p)

Number of combinations of n dissimilar things taken 'r' at a time in which 'p' particular things will never occur is (n–p)Cr

PERMUTATIONS

Number of arrangements of n different objects taken ‘r’ at a time.

If the order does matter it is a Permutation.

A Permutation is an ordered Combination.

Permutations of n different things taken 'r' at a time is denoted by nPr

The total number of arrangements of n things taken ‘r’ at a time, in which a particular thing always occurs = (n–1)P(r–1).

The total number of permutations of n different things taken ‘r’ at a time in which a particular thing never occurs = (n–1)Pr.

The number of arrangements when p of them are of one kind, q of another kind, r is still of another kind and so on, the total number of permutations is given by
n!/(p! q! r !.......)

Number of circular permutations of n things all taken at a time = (n – 1)!

Number of circular permutations of n different things taking ‘r’ at a time =nPr/r

Other Results:

nC0=1

nCn=1

nCr=nCn-r

nCr+nC(r-1)=(n+1)Cr