A poll is give , showing 40% are in favor of a new building project.If...

Step 1
We will use binomial probability to solve this question.
The formula for the binomial probability is:
${\displaystyle P\left(x\right){=}^n{C}_x\cdot p^x\cdot {(1-p)}^x}$, where
${\displaystyle n=}$ sample size
${\displaystyle p=}$ probability of success.
Given:
${\displaystyle n=6}$,
${\displaystyle p=40\mathrm{\%}=0.40}$
${\displaystyle x=3}$
Step 2 We need to find ${\displaystyle P(x=3)}$. The calculations are shown as follows:
${\displaystyle P(x=3){=}^6{C}_3\cdot {0.40}^6\cdot {(1-0.40)}^{6-3}}$
${\displaystyle =0.0177}$
Therefore, the probability that exactly $3$ of them favor the new building project is ${\displaystyle =0.0177}$.