Latihan SPM Permutations and Combinations

 

SEKOLAH MENENGAH KEBANGSAAN AGAMA MAAHAD MUAR ADDITIONAL MATHEMATICS FORM 5 PERMUTATIONS AND COMBINATIONS

SPM 2009

(PERMUTATION) 

22. There are 4 different Science books and 3 different Mathematics books on a shelf. Calculate the number of different ways to arrange all the books in a row if  (a) no condition is imposed, (b) all the Mathematics books are next to each other. [4 marks] {Ans: (a) 5040, (b) 720} SPM 2008

(PERMUTATION) 

23. Diagram 23 shows six numbered cards.

3

5

6

7

8

9

Diagram 23 A four digit number is to be formed by using four of these cards. How many (a) different numbers can be formed? (b) different odd numbers can be formed?

[4 marks] {Ans: (a) 360, (b) 240}

SPM 2007

(COMBINATION) 

23. A coach wants to choose 5 players consisting of 2 boys and 3 girls to form a badminton team. These five players are chosen from a group of 4 boys and 5 girls. g irls. Find (a)  the number of ways the team can be formed, (b)  the number of ways the team members can be arranged in a row for a group photograph, if the three girls sit next to each other. [4 marks] {Ans: (a) 60, (b) 36} SPM 2006

(PERMUTATION) 

22. Diagram 9 shows seven letter cards.

U

N

I

F

O

R

Diagram 9 A four letters code is to be formed using four of these the se cards. Find (a)  the number of different four-letter codes that can be formed, (b)  the number of different four letter codes which end with a constant.

M

[4 marks] {Ans: (a) 840, (b) 480}

 

  SPM 2005

(COMBINATION)

22. A debating team consists of 5 students. These students are chosen from 4 monitors, 2 assistant monitors and 6 prefects. Calculate the number of different ways the team can be formed if  (a)  there is no restriction, (b)  the team contains only 1 monitor and exactly 3 prefects. [4 marks] {Ans: (a) 792, (b) 160} SPM 2004

(PERMUTATION) 

23. Diagram 6 shows five cards of different letters.

H

E

B

A

T

Diagram 6 (a)  Find the number of possible arrangements, in row, of all the cards, (b)  Find the number of these arrangements in which the letters E and A are side by side.

[4 marks] {Ans: (a) 120, (b) 48}

SPM 2003

(PERMUTATION) 

22. Diagram 6 shows 5 letters and 3 digits.

A B C D E 6 7 8 Diagram 6 A code is to be formed using those letters and digits. The code must consist of three letters followed by 2 digits. digi ts. How many codes can be formed if no letter or digit is repeated in each code? [3 marks] {Ans: 360}