[求助]一道probabilities的题目。。Gr 12 math(大家没事进来看看)|『海外生活』 - 『漫游』酷论坛

[求助]一道probabilities的题目。。Gr 12 math(大家没事进来看看)

silverpin@2004-03-30 10:13

How many different 4-digit numbers are there such that the number is even, none of the digit repeat and first digit is not zero

用combinations 算
答案是2296

这么久没来, 一来就求助, 真是不好意思, 不过我实在算不出答案, 希望大家帮一下, 谢谢了

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Arael@2004-03-30 12:33

5*7*8*5 + 4*7*8*4 = 2296

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Arael@2004-03-30 12:37

some explanation:

two cases: first digit is

odd : 5 for the first digit
5 for the last digit
8*7 for the middle two digits

even: 4 for the first digit
4 for the last digit
8*7 for the middle two digits

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Lizard@2004-03-30 13:10

How many different 4-digit numbers are there such that the number is even, none of the digit repeat and first digit is not zero
# of ways
=total - 4-digit odd numbers
=( 9 ) ( 9 ) ( 8 ) ( 7 ) - ( 8 ) ( 8 ) ( 7 ) ( 5 )
=2296

explanation...10 numbers to choose: 0-9

total:
1st digit--> 9 choices (eliminate 0)
2nd digit--> 9 choices (u've already chosen one number for the 4th digit)
3rd digit--> 8 choices (chosen 2 already, 8 left)
4th digit--> 7 choices (chosen 3 already, 7 left)

odd:
4th digit-->5 choices (1,3,5,7,9)
1st digit-->8 choices (9 numbers remained, yet u cannot use 0 for this )
2nd digit-->8 choices (chosen two already)
3rd digit-->7 choices left

wish me good luck,
im having a test on binomial theorem tomorrow...

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silverpin@2004-03-30 13:27

*moved* A大。。。蜥蜴J。。。。
太感激了， 253~