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  • The number of five-digit numbers which are divisibie by 3 that can be formed by using the digits 1,2,3,4,5,6,7, 8 and 9 , when repetition of digits is allowed, is  <div clas

The number of five-digit numbers which are divisibie by 3 that can be formed by using the digits 1,2,3,4,5,6,7, 8 and 9 , when repetition of digits is allowed, is

 

Option: 1

3^9


Option: 2

4.3^8


Option: 3

5.3^8


Option: 4

7.3^8


Answers (1)

best_answer

1^{\text {st }}blank can be filled in 9 ways                                     2^{\text {sd }} blank can be filled in 9 ways (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 3 n+1, than fill the last blank by 2,5 or 8 .
If their sum is in the form 3 n+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.
\therefore Number of five-digit numbers = 9 \times 9 \times 9 \times 9 \times 3=3^9

Posted by

Rakesh

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