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Lenormand - Combination
Lenormand - Combination
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SVPrecis_11 _Permutation _Permutation and Combination Combination PROBLEM BASED ON PERMUTATION
1. If n n , find 2.
find If n
3. If = 6480, find 4.
find
find 5. 6. Find the total numbers of nine digits numbers which which have all different digits. digits. 7. How many even numbers numbers of four digits can be formed with the digits no digit being used more then once? 8. Find the number of numbers lying between 300 300 and 4000 that can be formed with the digits no digits being repeated. 9. Find the number of numbers of six digits formed the digits in which 5 always occurs in the tens place. 10. How many numbers can be formed by using any number of the digits 11. How many even numbers of 5 digits can be formed with the digits and 12. Find the sum of the 5 digit numbers which can be formed with the digits using each digit only once in each arrangement. 13. Find the sum of all 4-digit numbers that can be formed with the digit 14. A servant has to post 5 letters and there are 4 letter boxes. In how many ways can he post the letters. 15. In how many ways can three prizes be given away to t o 5 students when each students is eligible for any number of the prizes? 16. Find the number of numbers fo 5 digits that can be formed with the digits if repetition of digit is allowed. 17. In how many ways 6 rings of different type can be had in 4 fingers? f ingers? 18. In a town the car plate number contain only three or four digit not containing the digit 0. What is the maximum number of cars than can be numbered? 19. In a dinner party there are 10 Indians, 5 Americans, and 5 Englishmen. In how many ways can they be arranged in a row so that all persons of the same nationality sit together? 20. There are two books each of three volumes and two books each of two volumes., in how many ways can the ten books be arranged on a table so that the volumes of same book are not separated? 21. In a class of students there are 4 girls and 6 boys. In how many ways can they be seated in a row so that all the four girls are not together. 22. Find the number of different arrangements (permutations) of the letters of the word „Banana‟. 23. There are 3 copies each of 4 different books. In how many ways can they be arranged on a shelf? 1
24. Find the number of permutations of the letters fo the word “Independence”. Find also the number of re-arrangements. 25. How How many different words can be formed with the letter of the word “MATHEMATICS”? in how many of them the vowels are together and consonants are together? 26. In how many ways can the letters of the word „violent‟ be arranged so that vowels occupy only the odd places? 27. Find the number of arrangements of the letters of the word „Delhi‟ if always comes before 28. In how many can men sit around a table? 29. A round table conference is to be held between 20 delegates of 20 countries. In how many ways can they and the host be seated if two particular delegates are always to sit on either side of the host. 30. In how many ways can 7 Englishment and 6 Indians sit down around a table so that no two Indians are together. 31. Seven girls forming a round are dancing. In how many ways can they t hey stand in the circle PROBLEM BASED ON COMBINATION 32. 33. 34. 35. 36. find 37. How many quadrilaterals can be formed joining the vertices of a polygon of sides? 38. There are 6 students a. In how many ways can they be seated in a line so that C and D do not not sit together? b. In how many ways can a committee committee of 4 be formed so as to always include C? c. In how many ways ways can a committee of 4 be formed so as to always always include C but exclude E? 39. There are stations on a railway line. The number of kinds of tickets printed (no return tickets) is 105. Find the number of stations. 40. There are 10 points in a plane out of which 5 are collinear. Find the number of quadrilaterals formed these having vertices at points. 41. A committee consisting of 2 men and 2 women is to be chosen from f rom 5 men and 6 women. In how many ways can this be done? 42. Out of 7 men and 4 ladies a committee of 5 is to be formed. In how many ways can this t his be done so as to include at least 3 ladies? 43. A person has 12 friends of whom 8 are relatives. In how many ways can he invite 7 friends such that at least 5 of them may be relatives? 44. From 5 apples, 4 oranges and 3 mangoes, how many selections of fruits can be made? 45. In an election for 3 seats there are 6 candidates. A voter cannot vote for more than 3 candidates. In how many ways ways can he vote? 2
MIXED PROBLEMS 46. How many words of 4 different letters can formed out 7 capital letters, lett ers, 3 vowels and 5 consonants if each word starts with a capital letter and contains at least one vowel. 47. How many different words of 4 letters can be formed f ormed with the letters of the word “EXAMINATION”? 48. How many words can be formed out 10 consonants and 4 vowels, such that each contains 3 consonants and 2 vowels? 49. A table has 7 seats, 4 being on one side facing the window and three being on the opposite. In how many ways can seven people be seated at the table if 3 people must sit on the side facing the window? 50. A tea party is arranged for 16 people along two sides of a long table with 8 chairs on each side. Four men wish to sit on one particle slide and two on the other side. In how many ways can they be seated?
