By using all the integers at a time of the number 9910099800, how many 10 digit numbers can be forme

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27 Mar 2012 total numbers

By using all the integers at a time of the number 9910099800, how many 10 digit numbers can be formed.

OPtion

1) 6300
2) 5032
3) 3780
4) 1580
5) 1420
6) 900
7) 780
8) 196
9) 94
10) none of these

Solution

6*9*8*7*6*5*4*3*2*1/4*3*2*1*4*3*2*1
here denominator is for the revision of 0 and 9 4-4 times
and 6 in the numerator is for the possibilities in the first place.

Correct Option: 3 Best Solution (6)

Viru Sihag   12 years AGO

we can change the first integer by 6 ways because there are 4 0's and next all integer chng 9! ways so the all ways are 6*9! but there are 4 0's and 4 9's so we can't distinguish all these so divide (4!*4!). The ans is 6*9!/(4!*4!)=3780.

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Datla Kanthi   12 years AGO

We have 4 digits 0,1,8,9 and repeated digits 0,9 each 4 times

0 cannot be in first place so we have 6 choices for it
from second to tenth place we can arrange in 9! ways
Now repeated numbers will be 4!*4!(for both zero and 9
So total possible numbers = 6*9!/(4!*4!)=3780

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chiru   12 years AGO

total no. of 10 digit numbers that can be formed by the 9910099800 is 10!/(4!*4!)=6300
which contains the numbers that starts with 0 also..
now there are 2520 no.'s are formed with the starting digit as 0..therefore 6300-2520=3780
hence option 3 is the reasonable one...thank u..

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Tijo Jose   12 years AGO

Since we need a 10-digit number, it cannot start with zero. So there are only 6 options for the leftmost digit.
The remaining 9 places can be filled in 9! ways. So, total 6*9! numbers. But out of them, due to repetition of 9s and 0s, some get counted multiple times. Since there are 4 9s and 4 0s, total distinct numbers formed = (6 * 9!) / (4! * 4!) = 3780

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Shilpa   12 years AGO

we make a 10 digit no so-
first digit not equal to zero.there are 6 non zero no. i.e. 999918 total 6 then any one of them comes on first place.
(6*9*8*7*6*5*4*3*2*1)=2177280
- - - - - - - - - -
now there are 4 nine and 4 zero. so above resultant should be divided by 4! * 4!
ie. 2177280/24*24 = 3780 Answer

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sridhar reddy   12 years AGO

(6*9!)/(4!*4!)
=3780

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