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 $=$ $20+140+560=720$