Mathematics - Permutation & Combination Question with Solution | TestHub

-----(5 blanks) $1^{st}$ blank can be filled in 9 ways $2^{nd}$ blank can be filled in 9 ways $\_\_\_\_$ since repetition is allowed. $3^{rd}$ blank can be filled in 9 ways $4^{th}$ blank can be filled in 9 ways Now, we have to fill the $5^{th}$ 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. ∴ Ans $=9\times 9\times 9\times 9\times 3=3^9$.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 3 n , 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. ∴ Ans $=9\times 9\times 9\times 9\times 3=3^9$.