Question

A seven digit number is in form of abcdefg (g, f, e, etc. are digits at units, tens, hundred place etc.) where

a < b < c < d > e > f > g. The number of such numbers are

• A. 1981
• B. 2009
• C. 1560
• D. 1870

Answer 1

Answer: (C)

1560

Answer 2

Sol. Cases :

(i)If d = 6 then seven digit numbers possible are = ⁵C₃. ³C₃

[as a,b,c can be choosen from 1,2,3,4 or 5 & similarly e,f,g can be choosen from the unused 2 digit which are less than 6 & 0 can be used]

(ii)If d = 7then numbers possible = $6C_{3}.^{4}C_{3}$

(iii)If d = 8 then numbers possible = $7C_{3}.^{5}C_{3}$

(iv)If d = 9 then numbers possible = $8C_{3}.^{6}C_{3}$ Add all cases