ewe 發問於 科學及數學數學 · 6 年前

一條數學15分help

Mary has notes of $10,$20 $50 $100 and $500 each in her wallet.

(a) if she chooses 2 notes,

(i) in how many ways can she get the notes?

(ii) in how many ways can she get more than $100?

(b) if she should choose at least 1 note ,

(i) in how many ways can she get the notes?

(ii) in how many ways can she get more than $100?

1 個解答

評分
  • 土扁
    Lv 7
    6 年前
    最愛解答

    (a)(i)

    Number of ways that she chooses 2 notes out of the 5 notes

    = 5C2

    = 5!/2!3!

    = 10

    (a)(ii)

    When she chooses 2 notes out of $10, $20 and $50, she gets not more than $100.

    Number of ways that she gets not more than $100

    = 3C2

    = 3!/2!1!

    = 3

    Number of ways that she gets more than $100

    = 10 - 3

    = 7

    ====

    (b)(i)

    For each of the 5 notes, she can choose or not choose (2⁵).

    She is NOT allowed to choose no card (-1).

    Number of ways that she get the notes

    = 2⁵ - 1

    = 32 - 1

    = 31

    (b)

    If she get NOT more than $100, she should choose or not choose notes only fromthe 3 notes of $10, $20 and $50 (2³),but she is NOT allowed to choose no card (-1).

    Number of ways that she gets NOT more than $100

    = 2³ - 1

    = 7

    Number of ways that she gets more than $100

    = 31 - 7

    = 24

    2015-03-27 04:22:03 補充:

    (a)(ii) Alternative method :

    To gets more than $100, She can either

    (1) choose one note from $100 and $500 (2C1), and choose one note from the rest 3 (3C1); or

    (2) choose both $100 and $500 (2C2)

    Number of ways that she gets more than $100

    = 2C1 × 3C1 + 2C2

    = 2 × 3 + 1

    = 7

    2015-03-27 04:38:57 補充:

    (b)(ii) Alternative method :

    To gets more than $100, She can either choose 1 note from $100 and $500 (2C1) or choose both (2C2).

    For the rest 3 notes, she can either choose or not choose (2³).

    Number of ways that she gets more than $100

    = (2C1 + 2C2) × 2³

    = (2 + 1) × 8

    = 24

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