11TH CBSE MATHS Permutations WORKSHEET

 

Q 1.     In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection ?

Q 2.     A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles ?

Q 3.     From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there ?

Q 4.     A mint prepares metallic calenders specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years ?

Q 5.     There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post ?

Q 6.     A coin is tossed five times and outcomes are recorded. How many possible outcomes are there ?

Q 7.     In how many ways can an examinee answer a set of ten true/false type questions?

Q 8.     A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock ?

Q 9.     There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each ?

Q 10.   There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a student buy: (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book ?

Q 11.   Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other ?

Q 12.   A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl ?

Q 13.   Twelve students compete in a race. In how many ways first three prizes be given ?

Q 14.   How many A.P.'s with 10 terms are there whose first term is in the set {1, 2,3} and whose common difference is in the set {1,2,3,4,5} ?

Q 15.   From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done ?

Q 16.   How many three-digit numbers are there with no digit repeated ?

Q 17.   How many three-digit numbers are there ?

Q 18.   How many three-digit odd numbers are there ?

Q 19.   How many different five-digit number licence plates can be made if         

(i) first digit cannot be zero and the repetition of digits is not allowed,

(ii) the first-digit cannot be zero, but the repetition of digits is allowed ?

Q 20.   How many four-digit numbers can be formed with the digits 3,5, 7, 8,9 which are greater than 7000, if repetition of digits is not allowed ?

Q 21.   How many four-digit numbers can be formed with the digits 3,5, 7,8,9 which are greater than 8000, if repetition of digits is not allowed ?

Q 22.   In how many ways can six persons be seated in a row ?

Q 23.   How many 9-digit numbers of different digits can be formed ?

Q 24.   How many odd numbers less than 1000 can be formed by using the digits 0,3,5,7 when repetition of digits is not allowed ?

Q 25.   How many 3-digit numbers are there, with distinct digits, with each digit odd ?

Q 26.   How many different numbers of six digits each can be formed from the digits 4,5, 6,7,8,9 when repetition of digits is not allowed ?

Q 27.   How many different numbers of six digits can be formed from the digits 3,1, 7, 0, 9,5 when repetition of digits is not allowed ?

Q 28.   How many four digit different numbers, greater than 5000 can be formed with the digits 1,2,5,9,0 when repetition of digits is not allowed ?

Q 29.   Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible ?

Q 30.   A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible ? Also, find the number of unsuccessful attempts to open the lock.

Q 31.   A customer forgets a four-digit code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3,5,6 and 9. Find the largest possible number of trials necessary to obtain the correct code.

Q 32.   In how many ways can three job is I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?

Q 33.   How many natural numbers not exceeding 4321 can be formed with the digits 1,2, 3 and 4, if the digits can repeat ?

Q 34.   How many numbers of six digits can be formed from the digits 0,1, 3, 5, 7 and 9 when no digit is repeated ? How many of them are divisible by 10 ?

Q 35.   If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes.

Q 36.   A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there ? How many possible outcomes if the coin is tossed four times? Five times? n times?

Q 37.   Find the number of ways in which 8 distinct toys can be distributed among 5 childrent.       

Q 38.   Find the number of ways in which one can post 5 letters in 7 letter boxes.

Q 39.   Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5.

Q 40.   Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball.

Q 41.   In how many ways can 5 different balls be distributed among three boxes ?

Q 42.   In how many ways can 7 letters be posted in 4 letter boxes ?

Q 43.   In how many ways can 4 prizes be distributed among 5 students, when

(i) no student gets more than one prize ? (ii) a student may get any number of prizes ?

(iii) no student gets all the prizes ?

Q 44.   How many numbers of four digits can be formed with the digits 1, 2,3,4,5 if the digits can be repeated in the same number ?

Q 45.   How many three digit numbers can be formed by using the digits 0,1,3,5,7 while each digit may be repeated any number of times ?

Q 46.   How many natural numbers less than 1000 can be formed from the digits 0,1,2,3, 4,5 when a digit may be repeated any number of times ?

Q 47.   A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Q 48.   How many five digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?

 

ANSWERS

1. 378              2. 600              3. 6                  4. 14             

5. 625              6. 32                7. 1024

8. 999              9. 512              10. (i) 30 (ii) 11         

11. 42              12. 42              13. 1320         

    14. 15

15. 42840        16. 648            17. 900        

    18. 450            

19. (i) 27216 (ii) 90000          20. 72        21. 48

22. 720            23. 9(9!)          24. 21              25. 60              

26. 720            27. 600            28. 48       

29. 151200      30. 720,719     31. 24            

 32. 6                33. 229            

34. 600,120     35. 216     

36. 8,16, 2"     37. 5⁸               38. 7⁵               39. 91             

40. 20 x4¹⁹          41. 243            42. 4⁷

43. (i) 5! (ii) 625 (iii) 620      44. 625            45. 100            

46. 215            47. 8                48. 336