How many 7 digit numbers can be formed with the digits 2,3,0,3,4,4,3?

Explanation

In the given digits, the digit 1occur thrice, digit 2 occur twice.
No. of ways to fill 7 places from the given 7 digits `= (7!)/(3!.2!) = 420`
but out of these 420 numbers, some numbers start with digit '0'
Numbers starting with `'0' = (6!)/(3!.2!) = 60`
`:.` Required numbers `= 420 - 60 = 360`.