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Flashcards in PMC Deck (20)
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1
Q

Number of permutations of n different items?

A

n!

2
Q

Number of permutations of r different items chosen from b different items

A

nPr= n!/(n-r)!

3
Q

Number of permutation of n items with p and q identical items

A

n!/p!q!

4
Q

Circular permutation ( clockwise and anti-clockwise different )?

A

(n-1)!

5
Q

Circular permutation ( clockwise and anti-clockwise same )

A

(n-1)!/2

6
Q

Number of combinations choosing r distinct items form n different items

A

nCr= n!/(n-r)!r!

7
Q

Choosing r items from n different items ( repetition allowed )

A

n+r-1 C r

8
Q

Combination of n objects always including p particular objects

A

n-p C r-p

9
Q

Number of combinations always excluding p particular objects

A

n-p C r

10
Q

Number of arrangement always including p particular objects

A

n-p C r-p . r!
; r = number of objects to be taken
p = no of particular objects to be taken

11
Q

Number of arrangement always excluding p particular objects

A

n-p C r . r!

12
Q

Number of arrangements with p particular objects always together

A

(n-p+1)!p!

; p= particular objects to be kept together

13
Q

Number of arrangements with p particular objects always separated

A

n-p+1 C p . p! . (n-p)!
; n= no of objects
p = number of objects to be separated

14
Q

Number of ways to select one or more objects

A

2^n-1

;n= no of objects

15
Q

Unequal division of non identical items

A
(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
16
Q

Unequal distribution of non identical items

A

(m+n+p)!/(m!n!p!) . 3!

17
Q

Equal division of non identical items

A

(mn)!/(n!)^m m!
; m= no of groups
n= no of objects in each group

18
Q

Equal distribution of non identical items

A

(mn)!/(n!)^m
; m= no of groups
n= no of objects in each group

19
Q

Division of identical items into groups ( empty groups allowed )

A

n+r-1 C r-1

20
Q

Division of identical items into groups ( identical ones not allowed )

A

n-1 C r-1