Question

All the five-digit numbers $N=abcde$ 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 $0)=126$
Total numbers starting with 1
$={}^8{C}_4=70$ (using }$2,3,4,5,6,7,8,9)$
$1_{----}$
Total numbers starting with $23$
$={}^6{C}_3=20$ (using $4,5,6,7,8,9)$
$23_{---}$
Total numbers starting with $245={}^4{C}_2=6$ (using $6,7,8,9)$
$245_{--}$
$97^{\text{th }}$ number $=24678$