Question

All the five-digit numbers $N=a b c d e$ having property $a< b< c< d< e$ are arranged in the increasing order of their magnitude. The $97^{\text {th }}$ number in the list does not contain the digit

• A. 4
• B. 5
• C. 7
• D. 8

Answer 1

Answer: (B)

All the possible number are
${ }^{9} C _{5}$ (none containing the digit $\left.0\right)=126$
Total numbers starting with 1
$={ }^{8} C_{4}=70 $ (using }$ \left.2,3,4,5,6,7,8,9\right)$
$1_{- - - - }$
Total numbers starting with $23$
$={ }^{6} C_{3}=20$ (using $ \left.4,5,6,7,8,9\right)$
$23_{- - - } $
Total numbers starting with $245={ }^{4} C _{2}=6$ (using $\left.6,7,8,9\right)$
$245_{- - }$
$97^{\text {th }}$ number $=24678$