Looking at the scenario,
it is either a person chosen is in favor of the project or not.(Either success or failure)
The outcome is independent
Thus, we would apply binomial distribution. It is expressed as
P(x) = nCx * p^x * q^(n - x)
Where
x = number of successes
p = probability of success
q = probability of failure
n = number of trials
From the information given
p = 35% = 35/100 = 0.35
q = 1 - p = 1 - 0.35 = 0.65
n = 7
x = 5
We wan to find P(x = 5)
Thus,
P(x = 5) = 7C5 * 0.35^5 * 0.65^(7 - 5)
P(x = 5) = 7C5 * 0.35^5 * 0.65^2
P(x = 5) = 0.0466
Thus, the probability that exactly 5 of them favor the new project is 0.0466