一條數學15分help

(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