Latest Elitmus Aptitude Question SOLUTION: How many 10-digit numbers have at least 2 equal digits?

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(#M40157212) ELITMUS Numerical Ability question Keep an EYE

How many 10-digit numbers have at least 2 equal digits?

Asked In Elitmus Sniper (7 years ago)

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Baishali Roy  (7 years ago)

Number of 10 digit numbers with no digit equal= 9*9!
Total 10 digit numbers are= 9*10^9
So, number of 10 digit no.s with at least 2 equal digit is->
(9*10^9)-(9*9!) (Ans).

Is this solution Helpfull? Yes (29) | No (2)  

Sanjib Badyakar   (7 years ago)

we have 10 digit and at least 2 digits are equal...

lets 1st digit as 1 so 1 _ _ _ _ _ _ _ _ _ so wthin 9 places atleast 1 place must be 1 so remaining 8 places we can fill it up with any digit(0-9)
which results you 10^8 possibilities.

Now lets 1st digit as 2 so 2 _ _ _ _ _ _ _ _ _ so within 9 places at least 1 place must be 2 so remaining 8 places we can fill it up with any digit(0-9)
which results you 10^8 possibilities.

so we will get 10^8+10^8+10^8+10^8+10^8+10^8+10^8+10^8+10^8 = 9*10^8

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saicharan  (7 years ago)

becoz........................there are two bags so we have check the probability among those bags =1/2..........

total bags=2,chance is 1 so 1/2.

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