I am compiling a short shiur for my shul on Rosh Hashanna. I plan on discussing some items related to the Judaic calendar, with a focus on some statistics that I can eventually put into Excel and / or chart.
Here are some stats that I'm seeking:
Frequency of the day of week that Pesach begins (I can determine the weekday for Rosh Hashanna from that)
Weekday pairs - I.e., if Rosh Hashanna is on Mon. this year, what possible weekdays could it be the following year? List or table should be for both regular & leap years
Frequency of 1st day Chanukah being on Friday
Frequency of 10 Tevet being on Friday
Frequency of each kevi'ah - If a table or chart for all of them (I think there are about 10 in total?) then something stating which is most and which is least common
Notable recent or upcoming (25 - 30 years before or after now) Judaic / Gregorian rare U.S. holiday coincidences. E.g. 1st day Hanuka 5774 coincided with Thanksgiving 2013. (I'm looking for "rare", here. Don't include Chanukah / XMas, Succot / Columbus Day or Shavu'ot / Memorial Day. These occur every few years. I realize that this list may not be easily available, so this is not a primary concern for me, but would be nice to have.)
If you can find one or more websites having this info, I appreciate it, greatly.