Permutation(urgent!!!!!!!)

[匿名]

2010-03-16 6:47 am

(1) how many even numbers less than 200 may be formed from the digits 1,2,3,4,5,6, if no digit may be repeated?

(2) Using the digits 0,1,2,3,4, find the possible number of positive integers composed of one, two, three, four or five digits that can be formed when the same digit may be repeated in each number. Note: except the 1-digit number 0, the leading digit of these integers cannot be zero.

更新1:

Answer: (1) 30 (2) Multiple Choice: A.1024 B.1275 C.3125 D.3905 E.4325

更新2:

re: tonyleung052: but i don't understand what is how each digit has 5 choices. can u explain please?

回答 (1)

用戶2053

2010-03-16 7:27 am

✔ 最佳答案

1) For 1 digit numbers :
2 , 4 , 6 total 3 numbers
For 2 digits numbers :
The last digit is 2 : Total 5 numbers
The last digit is 4 : Total 5 numbers
The last digit is 6 : Total 5 numbers
Total 15 numbers
For 3 digits numbers :
The leading digit must be 1 (one case), the last digit is 2 , 4 or 6(three cases) ,
The middle have 4 possible cases.
Total 1 * 4 * 3 = 12 numbers
There are 3 + 15 + 12 = 30 even numbers less than 200

2)We use a special five digits number to represent these 1 to 5 digits numbers :
For example : 3 = 00003 , 0 = 00000
314 = 00314 , 2004 = 02004 , 12344 = 12344 etc.
For each digits there are 5 choices ,
so there are 5^5 = 3125 numbers can be formed.
Ans : C

2010-03-16 00:05:21 補充：
For a special five digits number , Each digit have 5 choices : 0 , 1 , 2 , 3 or 4

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