Question

The number of $7$ digit integers $abcdefg,$ where $a<b<c<d>e>f>g$ such that $a,b,c,d,e,f,g\in \left\{1,2,3,....,9\right\}$ , are

• A. $700$
• B. $20$
• C. $720$
• D. $800$

Answer 1

Answer: (C)

Case $\left(1\right):$ $d=7$
${}^6{C}_3{\times }^3{C}_3=20$
Case $\left(2\right):$ $d=8$
${}^7{C}_3{\times }^4{C}_3=140$
Case $\left(3\right):$ $d=9$
${}^8{C}_3{\times }^5{C}_3=560$
Total $=$ $20+140+560=720$