# 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.

• 8

For any four digit number to be formed from the digits 1,3,3,0 the first digit cant be 0.

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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)

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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).

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For the third digit there are 2 possibilties (3,0) are there. [ lets say 3 has been used up for 3rd digit]

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And lastly one digit will be left (0) for the fourth digit..

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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

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• -23
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