Let the digits a ,   b ,   c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

Step-by-step solution

Three numbers a ,   b ,   c are in A.P. ad they are used to making 9 - digit number using each digit thrice such that atleast three consecutive digits are in A.P., So, c , b , a will also be in A.P. Now, we have 7 position to put a , b , c   or   c , b , a as _     _     _     _     _     _     _ ⏟ 7   positions     _     _     . Number of such numbers is = C 1 2 · C 1 7 · 6 ! 2 ! &#183