The total number of people is 16 (7 men + 9 women). We need to find the probability that all 6 people chosen are women.
The number of ways to choose 6 women from 9 is given by the combination formula: \(\binom{9}{6}\).
The total number of ways to choose 6 people from 16 is given by: \(\binom{16}{6}\).
The probability that there are no men on the committee is:
\(P(\text{no men}) = \frac{\binom{9}{6}}{\binom{16}{6}}\)
Calculating these values:
\(\binom{9}{6} = 84\)
\(\binom{16}{6} = 8008\)
Thus, \(P(\text{no men}) = \frac{84}{8008} = \frac{21}{2002} = \frac{3}{286} \approx 0.0105\)
Alternatively, using the probability method:
\(P(\text{no men}) = \frac{9}{16} \times \frac{8}{15} \times \frac{7}{14} \times \frac{6}{13} \times \frac{5}{12} \times \frac{4}{11} = 0.0105\)
