PERMUTATION & COMBINATION For (COMPETITIVE EXAMS)

Permutation & Combination

                  FOR

   COMPETITIVE EXAMS

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1) From 5 consonants, 4 vowels and 3 capital letters, the number of of words beginning with a capital letter and containing 3 consonants and 2 vowels that can be made is

2) The Number of ways in which 10 boys and 10 girls can be seated in a row so that boys and girls are aternate is..

3) The Number of zeros at the end of non zero digits of 100! is

4) If 7 points out of 12 are in the same straight line, then the number of triangles formed is..

5) The Number of ways in which 10 examination papers can be arranged so that the best and the worst papers come together is .

6) Raja,Usha,Rani, Sonu are to give speeches in a class. The teacher can arrange the order of their presentation in..

7) How many different arrangements can be made out of the letters in the expansion A²B³C⁴, when written in full ?

8) The number of positive integers satisfying the inequality

ⁿ⁺¹Cₙ₋₂ - ⁿ⁺¹Cₙ₋₁ ≤ 100 is

9) If N is the number of positive integral solutions of x₁x₂x₃x₄=770. Then find N.

10) How many Numbers greater than 23000 cab be formed the digits 1,2,3,4,5 ?

11) Eleven animals of a circus have to be placed in eleven cages one in each cage. If 4 of the each cages are too small for 6 of the animals, find the number of ways of caging the animals.

12) How many six digits odd number greater than 600000 can be formed the digits 5,6,7,8,9,0 if

a) Repetition are not allowed

b) repetition are allowed

13) Find the number of different permutations of the letters of the word BANANA.

14) How many words can be formed out of the letters of the word ARTICLE so that vowels occupy the even places.

15) How many different words ending and beginning with a consonants can be made out of the letters of the word EQUATION

16) How many different words can be formed from the letters of the word INTERMEDIATE? In how many of them, two vowels never come together ?

17) How many different permutations can be formed from the letters of the word EXAMINATION taken four at a time.

18) How many different words can be formed with the letters of the word HARYANA? In how many of these H and N are together and how many of these begins with H and end with N ?

19) Prove that only 18 Numbers can be formed by using all the digits 1,2,3,4,3,2,1 so that the odd digits always occupy the odd places.

20) There are 3 copies each of 4 different books. In how many ways can they be arranged in a shelf ?

21) A round table conference is to be held between 20 delegates of 2 countries. In how many ways can they be seated if two particular delegates are.  a) Always sit together. b) never sit together

22) 20 persons are invited in a party. In how many ways can they and the host be seated at a circular table ? In how many of these ways will two particular persons be seated on either side of the host ?

23) In an examination a candidate has to passs in each of the papers to be successful, It the total number of ways to failis 63, how many papers are there in the examination ?

24) The total number of selections from 4 boys and 3 girls if each selection has to contain at least one boy is ?

The sum of all five digit number that can be formed using the digits 1,2,3,4 and 5(Repetition not allowed

25) Four boys picked up 30 mangoes. The number of ways in which they can divide them if all mangoes be identical, is

26) The Number of ordered triplets of positive integers which are solutions of the Equation x+y+z=100 is

27) A parallelogram is cut by two sets of m lines parallel to its sides. The number of parallelogram then formed is.

28) The Number of ways in which r letters can be posted in n letter boxes in a town is ..

29) The Number of lines of drawn through 6 points lying on a circle is.

30) The Number of divisors of 9600 including 1 and 9600 are…

30) The maximum number of points of intersection of 8 straight lines is..

31) The Number of signals that can be sent by 5 flags of different colours taking one or more at a time is..

32) The Number of different words that can be formed from the letters of the word PENCIL so that no two vowels are together is…

33) Let E=[⅓ +1/50]+[⅓+2/50]+.... up to 50 terms, then E will be…

34) Let S be set of all functions from the set A to the set A. If n(A)=k then n(S) is..

35) The Number of Numbers of 9 different non-zero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than that in the middle is.

36) ABCD is quadrilateral 3,4,5,6 points are marked on the sides AB,BC,CD,DA respectively. The number of triangles with vertices on different sides is.

37) Total Number of 6 digits Numbers in which all the odd digits and only odd digits appear is.

38) Total Number of Numbers greater than a million that can be formed with the digits 2,3,0,3,4,2,3 is

37) Total Number less than 3x10^8 and can be formed using the digits 1,2,3 is equal to

38)  If all the permutations of the letters in the word OBJECT are arranged (and numbered serially) in alphabetical order as in a dictionary, then the 717th word is..

39) In a three-storey building, there are four rooms on the ground floor, two on the first and two on the second floor. If the rooms are to be allotted to six persons, one person occupying one room only, the number of ways in which this can be done so that no floor remains empty

40) The total number not more than 20 digits that are formed by using the digits 0,1,2,3 and 4 is…

41) The Number of ways in which we can select four numbers 1 to 30 so as to exclude every selection of four consecutive Numbers is.

42) The Number of words of four letters containing equal number of vowels and consonants, where repetition is allowed, is.