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Schubert, Valenzuela in US women's Amateur final

Sophia Schubert and Albane Valenzuela advanced to the finals of the 117th U.S. Women's Amateur Championship on Saturday and hope to end long droughts in Sunday's 36-hole final at the … Click to Continue »
[08-17] Join us this evening as the #England #Lionesses take on the Netherlands in UEFA Womens European Championships Semi Final. Kick Off: 19:45.⚽️
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Correct logic of permuting 5 men and 5 women to find probability of different highest women rank
The problem reads like this: Problem Five men and $5$ women are ranked according to their scores on an examination. Assume that no two scores are alike and all $10!$ possible rankings are equally likely. Let $X$ denote the highest ranking achieved by a woman. (For instance, $X = 1$ if the top-ranked person is female.) Find $P(X = i),i = 1, 2, 3, . . ., 8, 9, 10$. Solution given was: $P(X=1)= \frac{5}{10}= \frac{1}{2}$ because there are 5 women and total of 10 to choose from $P(X=2)=\frac{5}{10}\times \frac{5}{9}=\frac{5}{18}$ because for rank1 thereare 5 men and total of 10 to choose from, for rank 2 (we want awoman) we still have 5 women but only a total of 9 to choosefrom. $P(X=3)=\frac{5}{10}\times \frac{4}{9}\times \frac{5}{8}=\frac{5}{36}$ $P(X=4)=\frac{5}{10}\times \frac{4}{9}\times \frac{3}{8}\times \frac{5}{7}=\frac{10}{168}$ $P(X=5)=\frac{5}{10}\times \frac{4}{9}\times \frac{3}{8}\times \frac{2}{7}\times \frac{5}{6}=\frac{5}{252}$ $P(X=6)=\frac{5}{10}\times \frac{4}{9}\times \frac{3}{8}\times \frac{2}{7}\times \frac{1}{6}\times \frac{5}{5}=\frac{1}{252}$ My solution was $P(X=1)=\frac{5\times 9!}{10!}=\frac{1}{2}$ because there are five women to occupy 1st rank and then there remained 9 which can permute in $9!$ ways. There are total $10!$ ways to permute $10$ people $P(X=2)=\frac{5\times \binom{5}{4}\times 8!}{10!}=\frac{5}{18}$ because there are five women to occupy 2st rank. The 1st rank will be of a man. So we have to select $4$ out of $5$ men which will be ranked after $2$nd rank. These four men and remaining 4 women can be permuted in $8!$ ways. $P(X=3)=\frac{5\times \binom{5}{3}\times 7!}{10!}=\frac{5}{72}$ $P(X=4)=\frac{5\times \binom{5}{2}\times 6!}{10!}=\frac{5}{504}$ $P(X=5)=\frac{5\times \binom{5}{1}\times 5!}{10!}=\frac{5}{6048}$ $P(X=6)=\frac{5\times \binom{5}{0}\times 4!}{10!}=\frac{1}{30240}$ Doubts Where my logic went wrong? When I compared the two approach, I realized that the books solution is permuting ranks higher than the highest ranked girl, while my solution is permuting ranks lower than the highest ranked girl. So I was guessing what makes book solution not permute lower ranks and my solution not permuting higher ranks. Shouldn't we permute on both sides of highest ranked girl?
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He published many other poems over the next ten years, including the popular The Lady of the Lake, printed in 1810 and set in the Trossachs. Portions of the German translation of this work were set to music by Franz Schubert. One of these songs, "Ellens dritter Gesang", is popularly labelled as "Schubert's Ave Maria".
Schubert, Valenzuela in US women's Amateur final
Sophia Schubert and Albane Valenzuela advanced to the finals of the 117th U.S. Women's Amateur Championship on Saturday and hope to end long droughts in Sunday's 36-hole final at the … Click to Continue »
In 1929 Nasos and I were in our final year at the Megareos School. We built a very simple AM transmitter tuned to about 500 metres and we broadcast the performance of a play acted by the final year students. I have no idea if anybody heard our transmission, but it was certainly the first amateur broadcast in Greece.
In the last few seconds of the final round, however, a little out of breath with his defensive display, the older man changed his tactics. With lowered head and ferocious face he advanced, a whirling bulk of might and action, upon the amateur. Tap--tap--tap! Left--right, over and under, through the guard and round the guard of the outfought youngster the unclenched gloves totted up a score of points. There was a careful restraint behind each blow, yet, when the gong sounded and they smilingly shook hands amid tumults of enthusiasm, a thin red stream was trickling from the right eyebrow of the amateur champion....
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