Question

A seven digit number divisible by 9 is to be formed by using 7 out of number {1,2,3,4,5,6,7,8,9}. The number of ways in which this can be done is

• A. $7!$
• B. $2\times 7!$
• C. $3\times 7!$
• D. $4\times 7!$

Answer 1

The correct option is D $4\times 7!$

$[1,2,3,4,5,6,7,8,9]$

$\Rightarrow 1,8$

$2,7$

$3,6$

$4,5$

There 4 pairs, whose sum is 9. from (1-9) and 1 is it say 9

No of ways :- ${}^4{C}_3{\times }^1{C}_1\Rightarrow 4$

No of arrangement $\Rightarrow 7!$

The total no of way $=4\times 7!$