Soal Permutasi dan Kombinasi

1. A bookshelf contains 5 German books, 7 Spanish books and 8 French books. Each book is different from one another. 

(a) How many different arrangements can be made of these books? 

(b) How many different arrangements can be made of these books if books of each language must be next to each other? 

(c) How many different arrangements can be made of these books if all the French books must be next to each other? 

(d) How many different arrangements can be made of these books if no two French books can be next to each other? 

2. Kode hadiah kupon belanja suatu toko swalayan berbentuk bilangan yang disusun dari angka 1,3,3,5,7. Jika kupon-kupon tersebut bedasarkan kodenya dari yang terkecil sampai dengan yang terbesar, maka kupon dengan kode lebih besar daripada 53000 sebanyak. . . 

3. In a group of 2 camels, 3 goats, and 10 sheep in how many ways can we choose a committee of 6 animals if 

(a) there are no constraints in species? 

(b) the two camels must be included? 

(c) the two camels must be excluded? 

(d) there must be at least 3 sheep? 

(e) there must be at most 2 sheep? 

(f) Joe Camel, Billy Goat and Samuel Sheep hate each other and they will not work in the same group. How many compatible committees are there? 

4. Seorang siswa diminta harus menjawab 10 dari 13 soal yang diberikan. Berapa cara mereka dapat memilih bila harus menjawab sedikitnya tiga dari lima soal yang pertama? 

5. There are 14 point on a semi circle, 8 points on the arc anf 6 point on the diameter. How many triangles can be formed by choosing any 3 points as their vertice? 

6. There is the word "INCREDIBLE" 

(a) Find the number of arrangement if vowel are adjacent each other 

(b) Find the number of arrangement if there are no adjacent vowels 

7. From the numbers 2, 3, 4,5, 6, 7, 8, 9 will be made with 3 different numbers. The number of distinct numbers that are greater than 640 but less than 860 is. . .  

8. A palindromic integer or palindrome is a positive integer whose decimal expansion is symmetric and that is not divisible by 10. In other words, one reads the same integer backwards or forwards. How many palindromes of 5 digits are even? 

9. The chess competition has 12 people, everyone must play each other in the first round. If winning gets 3 points, losers get -1 and the draw gets 1 point. How many points total for all players in the first half? 

10. Ten people will travel in two cars, each with a capacity of 6 people and 7 people. If each car must contain at least 2 people, then how many arrangement they will distribute in the two cars are .... 

11. Mr. Andi forgets the 4 digit combination to lock of his save. He only remembers that none of digits is 0 and the sum of all 4 digits is 9. How many times does he have to attempt to open the save? 

12. In how many ways can the letters of the word MURMUR be arranged without letting two letters which are alike come together? 

13. The 10 members in a Clean and Green Committee are made up of 5 married couples 

(a) The committee members are to be seated at a round table for a meeting. there are 3 members who form the executive subcommittee. Find the number of ways the 10 members can be seated if i. each couple must sit together ii. no 2 members of the executive subcomittee sit next to each other 

(b) The committee has to take a photgraph after the meeting. Find the number of ways they can be arranged in a row if all the men are together while all the women are together and no husband must be next to his wife. 

14. A group of 8 friends sit together in a circle. Ani, Budi and Cita are three members of this group 

(a) If Ani refuses to sit beside Budi, unless Cita sits on the other side of Ani as well, how many possible seating arrangement can there be? 

(b) Two latecomers then come to join he group, and they have to sit apart from each other. How many possible seating arrangement can there be, bearing mind the condition from (a)