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# The number of n digit numbers which consists of the digit 1 & 2 only if each is to be used at least once, is equal to 510 then n is equal to_____ (A) 7 (B) 8 (C) 9 (D) 10 Please explain step by step.

Arun Kumar IIT Delhi
$no. with atleast once occurrence \\=>total -no occurrence of 1 -no occurrence of 2 \\=>2^n-2=510 \\=>2^n=512 \\=>n=9$