Question

All five digit odd numbers formed using digits 0, 1, 2, 3, 4, 5 (without repeating any digit) are arranged in increasing order. Let sum of all digits of 151th number be 'a'. Value of a-7 is

Answer 1

First number is 10235
Number starting with 1, $\left(1\right),\underset{–}{4},\underset{–}{3},\underset{–}{2},\underset{–}{2}\to 4\times 3\times 2\times 2=48$
Number starting with 2, $\left(2\right),\underset{–}{4},\underset{–}{3},\underset{–}{2},\underset{–}{3}\to 4\times 3\times 2\times 3=72$
Number starting with 30, $\left(30\right),\underset{–}{3},\underset{–}{2},\underset{–}{2}\to 3\times 2\times 2=12$
Number starting with 31, $\left(31\right),\underset{–}{3},\underset{–}{2},\underset{–}{1}\to 3\times 2\times 1=6$
Number starting with 32, $\left(32\right),\underset{–}{3},\underset{–}{2},\underset{–}{2}\to 3\times 2\times 2=\underset{–}{12}\underset{–}{150}$
So 151th number is $\underset{–}{34015}$
So sum of digits is - $3+4+0+1+5=13$