how many no. of 4 digits can be formed with the digits 1,3,3,0.find their sum
0 cannot be first digit .So either 1 or 3 can be in thousands place.
case 1: 1 in thousand place
3,3,0 can be arrange in 3×2×1 / 2! ways = 3 ways i.e 1330,1303,1033.
case 2: 3 in thousand place
1,0,3 can be arrange in 3×2×1 ways =6 ways i.e 3103,3130,3310,3301,3013,3031
You sum up these 9 numbers and will get the result.
Hope this would have cleared your doubt.
For any four digit number to be formed from the digits 1,3,3,0 the first digit cant be 0.
Hence for the first digit there are only 3 possibilities are there.[1,3,3] (lets say 1 has been taken up for first place)
For the second there are again 3 since one of 1,3 and 3 will be used up for first place(we chose it to be 1)and 2 will be left (3,3) along with 0 for second digit. So for second digit 3 possibilities are there. [3,3,0] (lets say 3 has been taken for 2nd place).
For the third digit there are 2 possibilties (3,0) are there. [ lets say 3 has been used up for 3rd digit]
And lastly one digit will be left (0) for the fourth digit..
Hence no. of 4 digit numbers formed will be the product of the possibilities for each place..
Therefore, the total no. of 4-digit numbers formed = 3 * 3 * 2 * 1 = 18 numbers