Permutation and Combination problems, Example and Formula

1. 
   

   In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

1. A. 360     
2. B. 480      
3. C. 720        Correct Answer
4. D. 5040      
5. E. None of these      

2.  

   
   

   How many words can be formed by using letters of the word ‘DELHI’?

1. A. 50     
2. B. 72      
3. C. 85      
4. D. 120        Correct Answer

3.  

   
   

   From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

1. A. 564     
2. B. 645      
3. C. 735      
4. D. 756        Correct Answer

4.  

   
   

   In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

1. A. 810     
2. B. 1440      
3. C. 2880      
4. D. 50400        Correct Answer

5.  

   
   

   Find the number of ways the letters of the word ‘RUBBER can be arranged?

1. A. 450     
2. B. 362      
3. C. 250      
4. D. 180        Correct Answer

6.  

   
   

   Find in how many different ways, the letters of the word ‘LEADING’ can be arranged in such way that the vowels always come together?

1. A. 548     
2. B. 426      
3. C. 720        Correct Answer
4. D. 790      

7.  

   
   

   Out of 5 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

1. A. 60     
2. B. 1200      
3. C. 5230      
4. D. 7200        Correct Answer

8.  

   
   

   A bag contains 2 white marbles, 3 black marbles and 4 red marbles. Find in how many ways, 3 marbles can be drawn, so that at least one black marble is included in each draw?

1. A. 64       Correct Answer
2. B. 52      
3. C. 58      
4. D. 36      

9.  

   
   

   In how many ways can the letters of the word 'LEADER' be arranged?

1. A. 72     
2. B. 144      
3. C. 360        Correct Answer
4. D. 720      

10.  

    
    

    Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

1. A. 210     
2. B. 1050      
3. C. 25200        Correct Answer
4. D. 21400      

11.  

    
    

    In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

1. A. 159     
2. B. 194      
3. C. 205      
4. D. 209        Correct Answer

12.  

    
    

    How many combinations are possible while selecting four letters from the word ‘SMOKEJACK’ with the condition that ‘J’ must appear in it?

1. A. 81     
2. B. 8!/2!      
3. C. 3!/2!      
4. D. 41        Correct Answer

13.  

    
    

    There are 30 people in a group. If all shake hands with one another , how many handshakes are possible?

1. A. 870     
2. B. 435        Correct Answer
3. C. 30!      
4. D. 29! + 1      

14.  

    
    

    On a railway line there are 20 stops. A ticket is needed to travel between any 2 stops. How many different tickets would the government need to prepare to cater to all possibilities?

1. A. 760     
2. B. 190      
3. C. 380        Correct Answer
4. D. 72      

15.  

    
    

    Mayur travels from Mumbai to Jammu in 7 different ways. But he is allowed to return to Mumbai by any way except the one he used earlier. In how many ways can he complete his journey?

1. A. 49     
2. B. 42        Correct Answer
3. C. 48      
4. D. 6      

16.  

    
    

    If  Suraj doesn’t want three vowels together, then in how many, can he arrange letters of the word 'MARKER'?

1. A. 500     
2. B. 720      
3. C. 240        Correct Answer
4. D. 360      

17.  

    
    

    There are 35 people in a group. There are 12 school girls, 10 school boys, 5 senior citizens and 8 babies in the group. The organizer of the group wants to select a school girl or a school boy as leader of the group. In how many ways can he do so?

1. A. 22       Correct Answer
2. B. 1/2      
3. C. 13      
4. D. 35      

18.  

    
    

    There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?

1. A. 180     
2. B. 256      
3. C. 386      
4. D. 435        Correct Answer

19.  

    
    

    A box contains 2 white, 3 black and 5 red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

1. A. 29     
2. B. 36      
3. C. 48      
4. D. 85        Correct Answer

20.  

    
    

    A person can go from place “P” to “Q” by 7 different modes of transport, but is allowed to return back to “P” by any mode other than the one used earlier. In how many different ways can he complete the entire journey?

1. A. 42       Correct Answer
2. B. 30      
3. C. 11      
4. D. 89      

21.  

    
    

    In how many different ways can the letters of the word ‘GEOMETRY’ be arranged so that the vowels always come together?

1. A. 720     
2. B. 4320        Correct Answer
3. C. 2160      
4. D. 40320      

22.  

    
    

    In how many ways can the letters of the word INDIA be arranged, such that all vowels are never together?

1. A. 48     
2. B. 42        Correct Answer
3. C. 28      
4. D. 36      

23.  

    
    

    In Cricket League, in first round every team plays a match with every other team. 9 teams participated in the Cricket league. How many matches were played in the first round?

1. A. 36       Correct Answer
2. B. 72      
3. C. 9!      
4. D. 9! - 1      

24.  

    
    

    In Daya’s bag there are 3 books of History, 4 books of Science and 2 books of Maths. In how many ways can Daya arrange the books so that all the books of same subject are together?

1. A. 9     
2. B. 6      
3. C. 8640      
4. D. 1728        Correct Answer

25.  

    
    

    A trekking group is to be formed having 6 members. They are to be selected from 3 girls, 4 boys and 5 teachers. In how many ways can the group be formed so that there are 3 teachers and 3 boys or 2 girls and 4 teachers?

1. A. 55       Correct Answer
2. B. 90      
3. C. 27      
4. D. 144      

26.  

    
    

    In a class, there are 15 students. During a Christmas party all of them shook hands with each other only once. How many handshakes took place in the class?

1. A. 120     
2. B. 210      
3. C. 105        Correct Answer
4. D. 55      

27.  

    
    

    A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?

1. A. 12/74     
2. B. 24/78        Correct Answer
3. C. 13/78      
4. D. None of these      

28.  

    
    

    How many words can be formed  by using all letters of word ALIVE.

1. A. 86     
2. B. 95      
3. C. 105      
4. D. 120        Correct Answer

29.  

    
    

    In how many ways can the letters of the word ENCYCLOPAEDIA be arranged such that vowels only occupy the even positions?

1. A. 453600       Correct Answer
2. B. 128000      
3. C. 478200      
4. D. 635630      

30.  

    
    

    A locker in bank has 3 digit lock. Mahesh forgot his password and was trying all possible combinations. He took 6 seconds for each try. The problem was that each digit can be from 0 to 9. How much time will be needed to by Mahesh to try all the combinations?

1. A. 90 minutes     
2. B. 120 minutes      
3. C. 60 minutes      
4. D. 100 minutes        Correct Answer

31.  

    
    

    A bank has 6 digit account number with no repetition of digits within a account number. The first and last digit of the account numbers is fixed to be 4 and 7. How many such account numbers are possible?

1. A. 10080     
2. B. 5040      
3. C. 890      
4. D. 1680        Correct Answer

32.  

    
    

    4 members form a group out of total 8 members.

    
    

    (i) In how many ways it is possible to make the group if two particular members must be included.
    (ii) In how many ways it is possible to make the group if two particular members must not be included?

1. A. 15 and 360     
2. B. 15 and 15        Correct Answer
3. C. 30 and 360      
4. D. 360 and 360      

33.  

    
    

    A briefcase has a number-lock system containing a combination of 3 digits (Each digit can be of numbers 0 to 8). If the correct combination is unknown, how much maximum time would be required to open the bag if each “trial” of combination takes 3 seconds?

1. A. 45.23 minutes     
2. B. 36.45 minutes        Correct Answer
3. C. 60.34 minutes      
4. D. 90.15 minutes      

34.  

    
    

    In a group containing 6 cows and 4 buffalos, 4 livestock are to be selected in such a way that at least 1 cow should always be present. How many way of doing that are possible?

1. A. 209       Correct Answer
2. B. 205      
3. C. 194      
4. D. 163      

35.  

    
    

    In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?

1. A. 3     
2. B. 30      
3. C. 64        Correct Answer
4. D. 84      

36.  

    
    

    There are 8 routes from London to Delhi. And there are 6 routes from Delhi to Tokyo. In how many different ways can Raj travel from London to Tokyo via Delhi?

1. A. 100     
2. B. 48        Correct Answer
3. C. 24      
4. D. 14      

37.  

    
    

    How many 3-letter words can be formed out of the letters of the word ‘CORPORATION’, if repetition of letters is not allowed?

1. A. 990     
2. B. 336        Correct Answer
3. C. 720      
4. D. 504      

38.  

    
    

    In how many ways can we arrange the word ‘FUZZTONE’ so that all the vowels come together?

1. A. 1440     
2. B. 6      
3. C. 2160        Correct Answer
4. D. 4320      

39.  

    
    

    On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done?

1. A. 3846     
2. B. 2880        Correct Answer
3. C. 900      
4. D. 90      

40.  

    
    

    Without repetition, using digits 2, 3, 4, 5, 6, 8 and 0, how many numbers can be made which lie between 500 and 1000?

1. A. 70     
2. B. 147      
3. C. 60      
4. D. 90        Correct Answer