Latest CAT Aptitude Question SOLUTION: How many 8 digit numbers can be formed with 0- to 9 if repetition is not allowed?which is divisible by 9?

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How many 8 digit numbers can be formed with 0- to 9 if repetition is not allowed?which is divisible by 9?

Asked In CAT pratibha (12 years ago)

Solved Vignesh Read Solution (2)

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Vignesh  (12 years ago)

181440 eight digits numbers can be formed.

Long Explaination :

Rule For the number to be divisible by 9, the digits must add up to a multiple of 9.

Here We have 10 digits = 0,1,2,3,4,5,6,7,8,9

0+1+2+3+4+5+6+7+8+9 = 45(which is divisible by 9).

To form a 8 digits numbers, we want to remove 2 digits from those 10digits. And that two digits must be add up to be a multiple of 9.

Therefore, possible 2 digits we omit which multiple by 9 are,
(0,9) (1,8) (2,7) (3,6) (4,5) =>(5 Sets are there)

When we omit (0,9) pair, possible ways to arrange a number = 8!

When we use (0,9) pair means, possible ways to arrange a 8digit number = 7(7!)

(Because, 0 is not placed in first position but it can placed in rest of 7 digits.)

That means, we have ONE choice(omitting 0,9) to placed 8! numbers.
And, we have FOUR choices for 7(7!) numbers.

Finally. we adding them = 8!+(4×7)(7!)
=8(7!)+28(7!)
=36(7!)
=36(7*6*5*4*3*2*1)
=36(5040)
=181440

So, 181440 eight digits numbers can be formed bu using 0-9 digits without repetition.

Is this solution Helpfull? Yes (12) | No (1)  

Vignesh  (12 years ago)

I guess 181440 eight digit numbers can be formed which is divisible by 9 by using digits from 0-9(repetition is not allowed)

Is this solution Helpfull? Yes (5) | No (1)  

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