Given $3n$ cards, each of them will be written with a number from the following sequence: $$2, 3, ..., n, n + 1, n + 3, n + 4, ..., 2n + 1, 2n + 2, 2n + 4, ..., 3n + 3$$with each number used exactly once. Then every card is arranged from left to right in random order. Determine the probability such that for every $i$ with $1\le i \le 3n$, the number written on the $i$-th card, counted from the left, is greater than or equal to $i$.
Problem
Source: 2010 Indonesia TST stage 2 test 2 p4
Tags: probability, combinatorics
samrocksnature
16.12.2020 08:13
May I ask where you get all these questions? I'd really like to know so I can practice.
parmenides51
16.12.2020 08:19
my source is this for Indonesia TSTs but these shall be found in contest collections after the admin put them, as I requested here
samrocksnature
16.12.2020 08:20
Holy moly are you like...a professional math contest archiver? Wow I'm bookmarking that, thanks so much.
parmenides51
16.12.2020 08:35
All those Indonesian TSTs have been posted or found already in links collected there in aops, so there is no need to repost them or look from the start. If you like geometry, you might my page interesting which currenty has more than 10000 geometry problems all with aops link. The menu there is drop down menu on top and the categories on the right side of the page. @below ok do not mess with parental controls (although my page is safe to navigate) I have also created inside aops two public forums Old High School Olympiads and Old Russian Math Olympiads, in order to post without limit problems and make richer aops' contest collections and geometry collections that you may find interesting inside aops are mentioned here
samrocksnature
16.12.2020 08:37
parmenides51 wrote: All those Indonesian TSTs have been posted or found already in links collected there in aops, so there is no need to repost them or look from the start. If you like geometry, you might my page interesting which currenty has more than 10000 geometry problems all with aops link. The menu there is drop down menu on top and the categories on the right side of the page. Wow...unfortunately, it's classified as a computer hacking website on my parental controls >_< (not blaming you or anything, parental controls are weird)