Find the total number of ordered triples $( a , b , c )$ of non-negative integers satisfying the following conditions. [4 points] (a) $a + b + c = 7$ (b) $2 ^ { a } \times 4 ^ { b }$ is a multiple of 8.
Find the total number of ordered triples $( a , b , c )$ of non-negative integers satisfying the following conditions. [4 points]\\
(a) $a + b + c = 7$\\
(b) $2 ^ { a } \times 4 ^ { b }$ is a multiple of 8.