Answer: [tex]\bold{\dfrac{1}{99}}[/tex]
Step-by-step explanation:
There are 5 men and 7 women, which is a total of 12 people. Finding the probability that none of the four people are women is the same as saying that all four people are men.
[tex]\dfrac{5\ men}{12\ total\ people}\ and\ \dfrac{4\ men\ remaining}{11\ people\ remaining}\ and\ \dfrac{3\ men}{10\ people}\ and\ \dfrac{2\ men}{9\ people}\\\\\\=\dfrac{5\times 4\times 3\times 2}{12\times 11\times 10\times 9}\\\\=\dfrac{(4\times 3)\times (2\times 5)}{12\times 11\times 10\times 9}\\\\=\dfrac{1}{11\times 9}\\\\=\dfrac{1}{99}[/tex]
