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

• 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