Five different digits from the setoff numbers `{1,2,3,4,5,6,7}` are written in random order. How many numbers can be formed using 5 different digits from set `{1,2,3,4,5,6,7}` if the number is divisible by 9?

Explanation

Sum of given digits =1+2+3+4+5+6+7=28
Two digits have to be taken out.
If the number formed by remaining 5 digits is divisible by 9, then the sum of digits must be divisible by 9.
If a and b are two number taken out, then a+b=10
`therefore a=3, b=7 " or" a=4, b=6`
Number comprises the digits {1,2,4,5,6} or {1,2,3,5,7}
`implies` Required numbers `=2xx5!=240`