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6.Permutation and Combination
normal
All the five digits numbers in which each successive digit exceeds its predecessor are arranged in the increasing order of their magnitude. The $97^{th}$ number in the list does not contain the digit:
A
$4$
B
$5$
C
$7$
D
$8$
Solution
All the possible number are $^{9} \mathrm{C}_{5}$ (none containing the digit $0$ $)=126$
Total numbers starting with
$1 = {\,^8}{{\rm{C}}_4} = 70$
${ \text { (using }2,3,4,5,6,7,8,9)} $
${\text { Total starting with }}$
$\qquad 23 = {\,^6}{{\rm{C}}_3} = 20$
$(\text { using } 4,5,6,7,8,9)$
${\text { Total numbers starting with }} $
$\qquad 245 = {\,^4}{{\rm{C}}_2} = 6$
${\rm{ 9}}{{\rm{7}}^{th}}{\rm{ number }} = $
Standard 11
Mathematics
