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The general solution is THIS :
P(exactly n will get the disease) =
for n = 0, 1, 2, 3, 4, 5, 6. (1)
(a) P(not more than 2 will catch the disease) = P(0) + P(1) + P(2).
At this point, use the formula (1). Calculate P(0), P(1) and P(2); then add.
(b) P(4 or more will catch the disease) = P(4) + P(5) + P(6).
At this point, use the formula (1), again. Calculate P(4), P(5) and P(6); then add.
Do the rest on your own.