$\text{ A seven digit number is in the form of }abc\mathrm{defg}(g,f,e,\text{ etc. are digits at units, tens, }$

$\text{ hundreds place etc.) where }a<b<c<d>e>f>g\text{ . Then the number of such possible }$numbers is

$The minimum value of d will be 4$

$\text{ i) If }d=4{\text{ , then the number of seven digit numbers possible is }}^3{\mathrm{C}}_3{\cdot }^4{\mathrm{C}}_3=4$

$\text{ [as }a,b,c\text{ can be chosen from }1,2\text{ or }3\text{ and similarly }e,f,g\text{ can be chosen from }0,1,2\text{ or }3\text{ ] }$

$\text{ ii) If }d=5{\text{ , then the number of seven digit numbers possible is }}^4{\mathrm{C}}_3{\cdot }^5{\mathrm{C}}_3=40$

$\text{ [as }a,b,c\text{ can be chosen from }1,2,3\text{ or }4\text{ and similarly }e,f,g\text{ can be chosen from }0,1,2,3\text{ or4 }]$

$\text{ iii) If }d=6{\text{ , then the number of seven digit numbers possible is }}^5{\mathrm{C}}_3{\cdot }^6{\mathrm{C}}_3=200$

$\text{ [as }a,b,c\text{ can be chosen from }1,2,3,4\text{ or }5\text{ and similarly }e,f,g\text{ can be chosen from }0,1,2,3,4 or 5]$

$\text{ iv) If }d=7{\text{ , then the number of seven digit numbers possible is }}^6{\mathrm{C}}_3{\cdot }^7{\mathrm{C}}_3=700$

$\text{ [as }a,b,c\text{ can be chosen from }1,2,3,4,5\text{ or }6\text{ and similarly }e,f,g\text{ can be chosen from }$$0,1,2,3,4,5,6\text{ or 7] }$

$\text{ v) If }d=8{\text{ , then the number of seven digit numbers possible is }}^7{\mathrm{C}}_3{\cdot }^8{\mathrm{C}}_3=1960$

$\text{ [as }a,b,c\text{ can be chosen from }1,2,3,4,5,6\text{ or }7\text{ and similarly }e,f,g\text{ can be chosen from }$$0,1,2,3,4,5,6\text{ or 7] }$

$\text{ vi) If }d=9{\text{ , then the number of seven digit numbers possible is }}^8{\mathrm{C}}_3{\cdot }^9{\mathrm{C}}_3=4704$

$\text{ [as }a,b,c\text{ can be chosen from }1,2,3,4,5,6,7\text{ or }8\text{ and similarly }e,f,g\text{ can be chosen from }$$0,1,2,3,4,5,6,7\text{ or }8]$

$\text{ Total number of numbers is }4+40+200+700+1960+4704=7608$ 

$\text{ Therefore, the correct answer is }\left(3\right)\text{ . }$