There are 25 people, consisting of 15 women and 10 men that are lined up in a random order. Find the probability that 7 women are in position 1 through 16, and a woman in position 17.
How to go about this problem?
[Math] Find the probability that the 8th woman to appear is in 17th position.
combinatoricsprobability
Best Answer
HINT: Choose $1$ woman from $15$ and put her to $17^{th}$ position. Then from the rest of $14$, choose $7$ of them; and from $10$ men choose $9$ of them and permute them in the positions $1-16$. Then, permute the rest of people in the positions $18-25$.
EDIT: Just to verify my answer with the other two answers, the answer is $$\frac{\dbinom{15}{1}\dbinom{14}{7}\dbinom{10}{9}16!8!}{25!} \approx 0.028$$