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    F5 C6 Permutation and Combination

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    Karmen Thum
    This document contains examples and questions related to permutations and combinations. It begins by providing examples of calculating the number of permutations of letters in a word and arrangements of a subset of those letters. Several practice questions are then presented involving permutations of digits to form numbers or arrangements of people. The document then shifts to examples and questions involving combinations, such as choosing a subset of items from a larger set. Finally, past SPM exam questions are provided involving permutations and combinations of letters, digits and people. The key calculations and concepts covered are permutations, combinations, arrangements, subsets and restricted selections.

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    F5 C6 Permutation and Combination

    Uploaded by

    Karmen Thum
    87 views4 pages
    This document contains examples and questions related to permutations and combinations. It begins by providing examples of calculating the number of permutations of letters in a word and arrangements of a subset of those letters. Several practice questions are then presented involving permutations of digits to form numbers or arrangements of people. The document then shifts to examples and questions involving combinations, such as choosing a subset of items from a larger set. Finally, past SPM exam questions are provided involving permutations and combinations of letters, digits and people. The key calculations and concepts covered are permutations, combinations, arrangements, subsets and restricted selections.

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    This document contains examples and questions related to permutations and combinations. It begins by providing examples of calculating the number of permutations of letters in a word and arrangements of a subset of those letters. Several practice questions are then presented involving permutations of digits to form numbers or arrangements of people. The document then shifts to examples and questions involving combinations, such as choosing a subset of items from a larger set. Finally, past SPM exam questions are provided involving permutations and combinations of letters, digits and people. The key calculations and concepts covered are permutations, combinations, arrangements, subsets and restricted selections.

    Copyright:

    © All Rights Reserved
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    87 views4 pages

    F5 C6 Permutation and Combination

    Uploaded by

    Karmen Thum
    This document contains examples and questions related to permutations and combinations. It begins by providing examples of calculating the number of permutations of letters in a word and arrangements of a subset of those letters. Several practice questions are then presented involving permutations of digits to form numbers or arrangements of people. The document then shifts to examples and questions involving combinations, such as choosing a subset of items from a larger set. Finally, past SPM exam questions are provided involving permutations and combinations of letters, digits and people. The key calculations and concepts covered are permutations, combinations, arrangements, subsets and restricted selections.

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    © All Rights Reserved
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    Download as doc, pdf, or txt
    of 4

    A.

    PERMUTATIONS
    1. Given the words PLACES. Find
    a. The number of ways of arranging all the

    c. The number of ways arranging all the alphabets in

    alphabets in the given word.

    the given word so that the first alphabet is a vowel

    Example Solution:
    6! = 6.5.4.3.2.1
    = 720
    b. The number of ways of arranging four of the

    d. Find the number of these arrangements in which

    alphabets in the given word so that last alphabet

    the letters E and A are side by side.

    is S
    Example Solution:
    The way to arrange alphabet S = 1
    The way to arrange another 3 alphabets= 5 P 3
    The number of arrangement = 1 x 5 P 3 = 60
    2. How many four- digit numbers can be formed without repetitions from the digits 1, 2, 3, 4, 5, and 7 if
    that number.
    a) are even number

    c) Consist of digit 5

    b) are odd number

    d) more than 4000

    B.

    COMBINATIONS

    Exercise B.1
    1. How many ways to choose 5 books from 20

    2. In how many ways can committee of 3 men

    different books

    and 3 women be chosen from a group of 7 men

    Example solution:

    and 6 women ?

    The number of ways=

    20

    C5

    = 15504

    Example Solution:
    The numbers of ways = 7 C 3 x 6 C 3

    = 700
    2. A set of 20 students is made up of 10 students from each of two different year groups. Five
    students are to be selected from the set, and the order of selection is unimportant. Find

    a. the total number of possible selections.


    b. the number of selection in which there are at least two student from each of the two yearsgroups.

    PAST YEAR SPM QUESTION


    2003, Paper 1 1.Diagram below shows 5 letter and 3 digits.

    A code is to be formed using those letters and digits. The code must consist of 3 letters followed by 2
    digits. How many codes can be formed if no letter or digit is repeated in each code ?

    2. A badminton team consist of 7 students. The team will be chosen from a group of 8 boys and 5 girls.
    Find the number of team that can be formed such that each team consists of
    i.

    4 boys

    ii.

    Not more than 2 girl

    [ 4 marks]

    2004, Paper 1 3. Diagram below five cards of different letters.

    i.

    Find the number of possible arrangements, in a row , of all the cards.

    ii.

    Find the number of these arrangements in which the letters E and A are side by side .

    2005, Paper 1 4. A debating team consists of 5 students. These 5 students are chosen from 4 monitors, 2
    assistant monitors and 6 prefects. Calculate the number of different ways the team can be formed if
    i.

    There is no restriction

    ii.

    The team contains only monitor and exactly 3 prefects


    [4 marks]

    ASSESMENT
    1. Find the number of the arrangement of all nine letters of word SELECTION in which
    i.

    The two letters E are next to each other

    ii.

    The two letters E are not next to each other

    Solution:

    2. Four girls and three boys are to be seated in a row. Calculate the number of possible arrangements
    i.

    if all the three boys have to be seated together

    ii.

    a boy has to be seated at the centre

    Solution:

    3. Calculate the number of four digit even number can be formed from the digits 3, 4, 5, 6 and 9 without
    repetitions.
    Solution:

    4. Three alphabets are chosen from the word WALID. Find the number of possible choice if
    i.

    The alphabet A is chosen

    ii.

    The alphabet A and D is chosen

    Solution:

    5. A bowling team consists of 8 person. The team will be chosen from a group of 7 boys and 6 girls. Find
    the number of team that can be formed such that each team consists of
    i.

    3 boys

    ii.

    Not more than 1 girl

    Solution:

    ANSWER
    Exercise A.1
    1. c) 240 d) 240
    2. a) 120 b) 240
    Exercise B.1
    2. a) 15504

    c) 240
    b) 10800

    Problem solving
    1. i) 40320

    ii) 141120

    2. i) 720 ii) 2160


    3. 72
    4. i) 6
    5 i) 210 ii) 6
    Past year question
    1. 360
    2. i) 700 ii) 708
    3. i) 120 ii) 48
    4. i) 792 ii) 160

    ii) 3

    d) 180

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