PMC Flashcards
Number of permutations of n different items?
n!
Number of permutations of r different items chosen from b different items
nPr= n!/(n-r)!
Number of permutation of n items with p and q identical items
n!/p!q!
Circular permutation ( clockwise and anti-clockwise different )?
(n-1)!
Circular permutation ( clockwise and anti-clockwise same )
(n-1)!/2
Number of combinations choosing r distinct items form n different items
nCr= n!/(n-r)!r!
Choosing r items from n different items ( repetition allowed )
n+r-1 C r
Combination of n objects always including p particular objects
n-p C r-p
Number of combinations always excluding p particular objects
n-p C r
Number of arrangement always including p particular objects
n-p C r-p . r!
; r = number of objects to be taken
p = no of particular objects to be taken
Number of arrangement always excluding p particular objects
n-p C r . r!
Number of arrangements with p particular objects always together
(n-p+1)!p!
; p= particular objects to be kept together
Number of arrangements with p particular objects always separated
n-p+1 C p . p! . (n-p)!
; n= no of objects
p = number of objects to be separated
Number of ways to select one or more objects
2^n-1
;n= no of objects
Unequal division of non identical items
(m!+n!+p)!/m!n!p! ; m= objects in one group n = objects in two group p= objects in third group m+n+p= total num of objects
