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Question
How many number of four digits can be formed with the digits 1, 3, 3, 0?
Solution
The given digits are 1, 3, 3, 0.
Total numbers that can be formed with these digits =\[\frac{4!}{2!}\]Now, these numbers also include the numbers in which the thousand's place is 0.
But, to form a four digit number, this is not possible.
∴ Numbers in which the thousand's place is fixed as zero = Ways of arranging the remaining digits (1,3 and 3) in three places =\[\frac{3!}{2!}\]
∴ Four digit numbers = Total numbers\[-\] Numbers in which the thousand's place is 0=\[\frac{4!}{2!}\]-\[\frac{3!}{2!}\]= 9
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