How many 7-digit number can be formed using the digits 1,2,0,2,4,2 and 4?
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There are 7 digits 1, 2, 0, 2, 4, 2, 4 in which 2 occurs 3 times, 4 occurs 2 times.
Number of 7 digit numbers =
3!×2!
7!
=420
But out of these 420 numbers, there are some numbers which begin with '0' and they are not 7-digit numbers.
The number of such numbers beginning with '0' =
3!×2!
6!
=60
Hence, the required number of 7 digit numbers = 420 - 60 = 360.
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