If the possible number of ordered trials ( m , n , p ) where m , n , p N such that 1 m 100,1 n 50 , 1 p 25 and 2^ m +2^ n +2^ p is divisible by 3 are k , then the value of k 6250 is

Step-by-step solution

Here 2^m+2^n+2^p=(3-1)^m+(3-1)^n+(3-1)^p=3 k+(-1)^m+(-1)^n+(-1)^p(k I) so that 2^ mi +2^ n +2^ p is divisible by 3 if m , n , p all are odd or all are even. Number of possible ordered triads =50 25 12+50 25 13=31250