F.6 Maths and Stat.

2010-08-07 5:57 pm

I'm recently preparing for my new school term and I find myself so stupid.
Get stuck in Chapter one.
Please help.

A three digit number is formed from the digits 0,1,3,5,6,7,8. Each digit can be used only once.
a. How many possible numbers can be formed?
b. How many of these are even numbers?
c. How many of these are less than 500?

Heartfelt thanks!

回答 (1)

用戶2053

2010-08-07 6:26 pm

✔ 最佳答案

a)The 1st digit can not be 0 ,so the 1st digit have 6 choices , other digits is formed from the remain 2 from 6 digits.6 * 6P2 = 180 numbers can be formed.Method 2 :All cases - the 1st digit is 0 cases= 7P3 - 6P2 = 180 numbers can be formed.
b)The last digits must be formed from 0 , 6 , or 8, other digits are formed from
other 2 from 6 digits ,3 * (6P2) = 90 of these are even numbers.c)The 1st digit must be 1 or 3 , 2 choices ,2 * (6P2) = 60 of these are less than 500.

2010-08-07 10:37:45 補充：
Corrections ,

b)

The last digits must be formed from 0 , 6 , or 8, other digits are formed from
other 2 from 6 digits ,

For the last digit is 0 ,

6P2 = 30 cases

For the last digit is 6 or 8 ,

The 1st digit have 5 choices since it can not be 0 ,

5 * 5P1 + 5 * 5P1 = 50 cases

Total 30 + 50 = 80 cases

Sorry!!

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