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The number of six-digit natural numbers that can be formed using the digits $2, 3, 4, 0, 5, 6, 7, 8$ (repetition of digits is allowed) is:

If all the possible $3$-digit numbers are formed using the digits $1, 3, 5, 7, 9$ without repeating any digit,then the number of such $3$-digit numbers which are divisible by $3$ is

$A$ vehicle registration number consists of $2$ letters of the English alphabet followed by $4$ digits,where the first digit is not zero. The total number of vehicles with distinct registration numbers is

The number of ways of arranging $8$ boys and $8$ girls in a row so that boys and girls sit alternately is

Find $r$ if $^{5}P_{r} = ^{6}P_{r-1}$.

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