Mathematics - Permutation & Combination Question with Solution | TestHub

-----(5 blanks)

$1{}^{\text{st }}$ blank can be filled in 9 ways

$2^{\text{nd }}$ blank can be filled in 9 ways $\_\_\_\_$ since repetition is allowed.

$3^{\text{rd }}$ blank can be filled in 9 ways

$4^{\text{th }}$ blank can be filled in 9 ways Now, we have to fill the

$5^{\text{th }}$ blank carefully such that the number is divisible by 3 . Add the 4 numbers in the first 4 blanks. If their sum is in the form 3n, then fill the last blank by 3, 6 or 9 so that the sum of all digits is divisible by 3.

If their sum is in the form $3n+1$, than fill the last blank by 2,5 or 8 .

If their sum is in the form $3n+2$, than fill the last blank by 1 , 4 or 7 .

Therefore, in any case, the last blank can be filled in 3 ways only. $\text{ ∴ Ans }=9\times 9\times 9\times 9\times 3=3^9.$