F.5 math's questions

2013-02-07 4:15 am
The questions are came from "New Senior Secondary Mathematics in Action
Compulsory Part" Chapter 9 "Permutation and Combination"

1. In a lottery, players are required to select 5 different numbers from 1 to 30
and mark them on a ticket.
(a) How many different lottery tickets can there be if the order of numbers is
counted? (Ans: 17100720)

(b) Suppose one extra number can be chosen from 1 to 30 after the 5 numbers
are chosen, and this extra umber can be one of the 5 previously selected
numbers. How many different lottery tickets of 6 numbers can there be if the
order of numbers is counted? (Ans: 513021600)

2. A student wants to take 4 courses in the coming academic year. There are 4 Mathematics courses (M1, M2,M3,M4) and 5 Finance courses (F1, F2, F3, F4,
F5).

(a) Due to a time clash, courses M1 and F2 cannot be taken together. How
many different choices are there? (Ans:105)

回答 (2)

2013-02-07 4:54 am
✔ 最佳答案
1a)30P5 = 30 * 29 * 28 * 27 * 26 * 25 = 17100720 different lottery tickets.
b)17100720 * 30 = 513021600 different lottery tickets.

2a)All choices - including M1 and F2 choices
= (4+5)C4 - 2C2 * (4+5-2)C2
= 9C4 - 2C2 * 7C2
= 126 - 21
= 105 different choices.

2013-02-06 22:45:30 補充:
1a)

30P5 = 30 * 29 * 28 * 27 * 26 = 17100720.
2013-02-08 9:37 am
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