Permutations and Combinations

MCQ's collected from all Engineering Entrance Examinations (Click here)


Important Formulas :


1.The number of permutations of   dissimilar objects taken   at a time is denoted by   or .


2.The number of permutations of   dissimilar objects taken   at a time is denoted by    


3.The number of permutations of   dissimilar objects taken   at a time is denoted by  


4.The number of permutations of   dissimilar objects taken   at a time is denoted by


5.The number of permutations of   dissimilar objects taken   at a time is denoted by


6.Permutations when repetitions are allowed  Let   and be positive integers such that .Then the number of permutations of    dissimilar things taken    at a time, when repetition of things is allowed any number of time, is .


7.Permutations when repetitions are allowed The number of permutations of    dissimilar things taken at a time with at least one repetition  is


8.Circular permutations : The number of circular permutations of dissimilar things taken all at a time is ( n-1 )!


9.Circular permutations : In case of hanging type circular permutations like garlands of flowers, chains of beads etc., the number of circular permutations of  things is .


10.Permutations of objects in which some are like and the rest are different :  The number of linear permutations of  things in which  P things are similar and the rest are dissimilar is


11.Permutations of objects in which some are like and the rest are different :  The number of linear permutations of  things in which   there are  similar things of one kind, similar things of second kind and the rest are dissimilar is


12.Combinations The number  of combinations of  dissimilar things  taken at a time is denoted by


13.Combinations


14.Combinations


15.Combinations For


16.Combinations For


17.Combinations If .


18.Combinations If .


19.If   similar things are of one kind , similar things  are of second kind and similar things are of third kind, then the number of ways of selecting any number of things   ( one or more) out of them is


20.The number of ways  of dividing dissimilar things into  two groups containing  and  thing is


21.The number of ways  of dividing , dissimilar things ( are ditinct) into three groups  of   (   things is


22.The number ways of dividing   dissimilar things into   equal groups is .


23.The number ways of  distributing     dissimilar things  equally to    persons is  .


24.The number of ways that   different things of one type and different things of a second type where can be arranged in a row so that no two things of the second type come together is .


25.If   are distinct primes and    are non-negative integers, then the number of positive integral divisors of   (this includes 1 and n.)


26.If   are distinct primes and    are positive integers, then the sum of distinct positive integral divisors of    is .


27.Highest power of a prime  in n! is   where denotes the integral part.


 

 


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