To calculate the probability of randomly selecting three women from a group consisting of six men and three women, we need to use combinatorics.

We approach this problem step-by-step:

1. Total number of people: 6 men + 3 women = 9 people.
2. Favorable outcomes: We need to select all 3 women from the group of 3 women.
   • The number of ways to select 3 women from 3 women is $\binom{3}{3} = 1$.
3. Total possible outcomes: The number of ways to select 3 people from 9 people is $\binom{9}{3}$.

Now, calculate $\binom{9}{3}$:

$\binom{9}{3} = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} = 84$

Thus, the total number of ways to select 3 people from 9 is 84.

4. Probability: The probability is the ratio of favorable outcomes to the total outcomes.

$\text{Probability} = \frac{\binom{3}{3}}{\binom{9}{3}} = \frac{1}{84}$

Thus, the probability of selecting 3 women is $\frac{1}{84}$.

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Would you like more details or clarifications on any step?

Here are 5 questions that expand on this problem:

1. How would the probability change if there were 4 women instead of 3?
2. How is the combination formula $\binom{n}{r}$ derived?
3. What is the probability of selecting 2 men and 1 woman?
4. How do combinations differ from permutations in this context?
5. What is the probability of selecting at least 1 woman when selecting 3 people?

Tip: In probability, combinations are used when the order of selection doesn't matter, whereas permutations are used when order matters.