If you have k trials that result in 5,6,7 with probabilities $P(5)$, $P(6)$, and $P(7)$ (respectively), with
$P(5) + P(6) + P(7) = 1$,
what is the probability that 5 and 6 occur at least once.
Would it be $1-P(\text{5 and 6 never occur}) = 1- (P(5)+P(6))^0(P(7))^n = 1 - P(7)^n$?