lie on a circle 
and point 
lies outside the circle. The given points are such that (i) lines 
and 
are tangent to 
are collinear, and (iii) 
.
bisects 
.
Y by
In a race among 5 snails, there is at most one tie, but that tie can involve any number of snails. For example, the result of the race might be that Dazzler is first; Abby, Cyrus, and Elroy are tied for second, and Bruna is fifth. How many different results of the race are possible?
This post has been edited 1 time. Last edited by Eternica, Mar 7, 2025, 5:14 PM
people in the tie is 
.
to 
gives 
.
.
.
and 
respectively, so the answer is
people, then there are 
ways to choose the people in the tie, and 
ways to arrange the people (the tied people are consider “one person). So, adding over all 
we get 
as desired.
