Permutation and Combination Formula

 1.  Arrangement : 

Number of permutations of n different things taken r at a time 

$ = ^nP_r = \frac{n!}{(n-r)!}$

2. Circular Permutation :

The number of circular permutations of n different things taken all at a time is;  

$(n-1)!$

3. Selection :

 Number of combinations of n different things taken r at a time 

$= ^nC_r =\frac{n!}{r! (n-r)!}= \frac{^nP_r}{r!}$

4. The number of permutations of 'n' things, taken all at a time, when 'p' of

them are similar & of one type, q of them are similar & of another type, 'r' of

them are similar & of a third type & the remaining n - (p + q + r) are all

different is $\frac{n!}{p!q!r!}$

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