The possible number of ordered triplets `(m,n,p)` where `m,n,p epsilon N` is `(6250k)` such that `1le-mle100,1lenle50,1leple25` and `2^(m)+2^(n)+2^(p)` is divisible by `3` then `k` is

Answer

5

Explanation

Here `2^(m)+2^(n)+2^(p)=(3-1)^(m)+(3-1)^(n)+(3-1)^(p)=3k+(-1)^(m)+(-1)^(n)+(-1)^(p)`
So that `2^(m)+2^(n)+2^(p)` is divisible by `3` if `m,n,p` all are odd or all are even
`implies` Number of possible ordered triplets
`=50xx25xx12+50xx25xx13=31250=6250xx5`