${}^nC_1 + {}^nC_2 .................. + {}^nC_n = 255$, then the value of n will be-

Explanation

We know- ${}^nC_0 + {}^nC_1 + {}^nC_2............+ {}^nC_n= 2^n$ ${}^nC_1 + {}^nC_2 + {}^nC_3............ {}^nC_n= 2^n - {}^nC_0$ According tothe question ${}^nC_1 + {}^nC_2............+ {}^nC_n= 255$ $2^n - {}^nC_0 = 255$ $2^n - 1= 255$ $2^n = 256 = 2^8$ Since, the bases on both sides are the same, the exponents are also same. n = 8