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sgoll
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Q. How many 5-digit positive integers exist where no two 17 Feb 2007, 21:04
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Q. How many 5-digit positive integers exist where no two consecutive digits are the same?

A.) 9*9*8*7*6
B.) 9*9*8*8*8
C.) 9^5
D.) 9*8^4
E.) 10*9^4



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trivikram
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Q. How many 5-digit positive integers exist where no two 17 Feb 2007, 21:34
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sgoll
Q. How many 5-digit positive integers exist where no two consecutive digits are the same?

A.) 9*9*8*7*6
B.) 9*9*8*8*8
C.) 9^5
D.) 9*8^4
E.) 10*9^4
Show more


1st digit can be 1 to 9 = 9 ways
2nd digit can be 0 to 8 = 9 ways (we consumed 1 digit already in the 1st didgit)
3rd digit can be 0 to 7 = 8 ways
4th digit can be 0 to 6 = 7 ways
5th digit can be 0 to 5 = 6 ways

Total # of numbers = 9*9*8*7*6 (A)
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prude_sb
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Q. How many 5-digit positive integers exist where no two 17 Feb 2007, 21:35
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sgoll
Q. How many 5-digit positive integers exist where no two consecutive digits are the same?

A.) 9*9*8*7*6
B.) 9*9*8*8*8
C.) 9^5
D.) 9*8^4
E.) 10*9^4
Show more


let the number be abcde

a can be 1-9 so 9 choices
b can be 0-9 but not same as a so 9 choices
c can be 0-9 but not same as b so 9 choices
so on for d,e

so ans is 9^5 - C
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trivikram
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Q. How many 5-digit positive integers exist where no two 17 Feb 2007, 21:37
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prude_sb
sgoll
Q. How many 5-digit positive integers exist where no two consecutive digits are the same?

A.) 9*9*8*7*6
B.) 9*9*8*8*8
C.) 9^5
D.) 9*8^4
E.) 10*9^4

let the number be abcde

a can be 1-9 so 9 choices
b can be 0-9 but not same as a so 9 choices
c can be 0-9 but not same as b so 9 choicesso on for d,e

so ans is 9^5 - C
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prude: Can you explain the thing in bold please? Thanks !
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prude_sb
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Q. How many 5-digit positive integers exist where no two 17 Feb 2007, 21:48
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trivikram
prude_sb
sgoll
Q. How many 5-digit positive integers exist where no two consecutive digits are the same?

A.) 9*9*8*7*6
B.) 9*9*8*8*8
C.) 9^5
D.) 9*8^4
E.) 10*9^4

let the number be abcde

a can be 1-9 so 9 choices
b can be 0-9 but not same as a so 9 choices
c can be 0-9 but not same as b so 9 choicesso on for d,e

so ans is 9^5 - C

prude: Can you explain the thing in bold please? Thanks !
Show more


a can be any number from 1 to 9
b can be anything other than 'a' so it can be any number from 0-9 other than a
c can be any number other than 'b' it can also be same as 'a'
similarly for d,e

32323 would be acceptable since we only need the consecutive integers to be different

choice A gives the number of cases where ALL digits are unique ...
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Q. How many 5-digit positive integers exist where no two 17 Feb 2007, 22:25
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Yes OA is C. Thanks for the detailed explanation prude_sb
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trivikram
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Q. How many 5-digit positive integers exist where no two 18 Feb 2007, 06:48
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Got it...Again read the question wrong....



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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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