Envelope Question: Five letters addressed to individuals 1,2,3,4 and 5 are randomly placed in five addressed envelopes, one letter in each envelope.

I’m trying to find the probability of:

  1. Exactly three letters go in the correct envelopes.
  2. Exactly two letters go in the correct envelopes
  3. No letters go in the correct envelopes

Here is my approach:

So there is clearly a total of 5! distinct ways of arranging the letters.

  1. If exactly three letters go in the correct envelopes, then there are $ 5 \choose 3$ ways of choosing the positions for the three correct envelopes, and for the remaining two letters, there are 2! ways of organizing them. Thus, probability = $ \frac{{5 \choose 3} * 2!}{5!}$ .

  2. If exactly two letters go in the correct envelopes, then there are $ 5 \choose 2$ ways of choosing the positions for the two correct envelopes, and for the remaining three letters, there are 3! ways of organizing them. Thus, probability = $ \frac{{5 \choose 2} * 3!}{5!}$ .

  3. I’m not really sure how to approach this problem.

Any input would be great.

How can I have more than five concurrent torrent downloading with transmission WD MyCloud?

How can I have more than five concurrent torrent downloading with transmission WD MyCloud? I’ve seen an article where I can edit the .json (How to have more than five torrents downloading concurrently with transmission?). But how do I access this on my WD MyCloud Nas Drive?

Five functions to get the digits of a number

I’m writing a simple function: given a number, it will return a sequence or a collection of the digits in the number (in the correct order). i.e (get-digits-fn 1234567) => (1 2 3 4 5 6 7) / [1 2 3 4 5 6 7]

Below are five attempts at the same function:

(defn get-digits-1 [num]   (->> [num '()]        (iterate (fn [[num digits]]                   (when (> num 0)                     [(quot num 10) (conj digits (rem num 10))])))        (take-while some?)        (last)        (second)))  (defn get-digits-2 [num]   (when (> num 0)     (lazy-seq (concat (get-digits-2 (quot num 10)) '((rem num 10))))))  ;; Suggested by Carcigenate (defn get-digits-3 [num]   (->> (str)        (map str)        (map int)        (into '())))  (defn get-digits-4 [num]   (loop [n num          res '()]     (if (= n 0)       res       (recur (quot n 10) (conj res (rem n 10))))))  (defn get-digits-5 [num]   (->>    (iterate (fn [[n digits]]               [(quot n 10) (conj digits (rem n 10))])             [num '()])    (drop-while #(not= 0 (first %)))    (first)    (second))) 

A helper function for testing performance:

(defn quick-bench-get-digits [fn range]   (quick-bench (->> range                     (map fn)                     (map (partial apply vector))                     (into [])))) 

The perf results (output truncated to only show execution time mean):

eul> (quick-bench-get-digits get-digits-1 (range 1 100000)) Execution time mean : 129.516521 ms  eul> (quick-bench-get-digits get-digits-2 (range 1 100000)) Execution time mean : 128.637055 ms  eul> (quick-bench-get-digits get-digits-3 (range 1 100000)) Execution time mean : 24.267716 ms  eul> (quick-bench-get-digits get-digits-4 (range 1 100000)) Execution time mean : 25.083393 ms  eul> (quick-bench-get-digits get-digits-5 (range 1 100000)) Execution time mean : 145.430443 ms 

It looks like get-digits-3 is the fastest while get-digits-4 is closely behind. (As the numbers increase, get-digits-3 outperforms get-digits-4. i.e try (range 1000000 2000000))

  1. Any way to increase performance more without leaving Clojure land?
  2. If mutability and Java inter-op is allowed, is there a way to increase performance?

p.s. functions 1 and 5 are almost identical. This was incremental exploration.

AWS Autoscaling Group won’t honor five minute draining policy of the Target Group when scaling down

We have an Autoscaling Group in AWS that we manually scale up and down at the time being. Our ASG is currently attached to one Target Group, which has all of our prod servers in it.

Before using the ASG, we would add and remove servers to the Target Groups manually from the Target Group console, and the nodes would deregister after draining properly. We have a very stateful application so the deregistration delay is really important for us.

Yesterday when scaling down through the ASG interface (specifically by asking for a lower number of desired instances), all the connections dropped instantly, which dropped hundreds of connections instantly instead of honoring the five minute draining policy of the target group.

How do I make my ASG honor my draining policy?

I have tried this: AWS ASG With Application LB and Connection Draining but it does not set the connections to “draining”, but just “terminating: waiting”, and my health checks are healthy so I don’t think it is actually stopping new connections/draining.

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How active are the animals in Kruger National Park (S. Africa) in August? Season to see the Big Five (elephant, rhino, lion, leopard, & buffalo)?

I just booked a trip to South Africa with the purpose of viewing wildlife in Kruger National Park (a safari has always been my dream!!) for August of 2018. I know that animals are unpredictable, but I also know that there are seasons in which the wildlife are more active.

Now August in South Africa, is still their winter time merging into spring, and I was wondering if this means it would be too early to have a chance of seeing all members of the big five (black rhinoceros, African elephant, water buffalo, African lion, African leopard) as well as hyenas, zebras, giraffes, etc.? Essentially, will the wildlife be less active in August or do they stay pretty active even in the winter months? Steady activity?

My Five Year Payment History Since FSB

Hey everyone. It's been a long while since I've been active here on the forums. I started with FSB in October 2012. I thought it would be interesting for some of you if I posted my entire 5 year payment history since then. It's far from amazing but I think demonstrates the value of FSB.

I spent a few months in the beginning focused on my sites and then got involved in other things and spent less and less time on them as months passed. Eventually I spent ZERO time on these sites and they…

My Five Year Payment History Since FSB

How many families constitue a Major Clan in Legend of the Five Rings

In Legend of the Five Rings, a list of families is presented for each Major Clan. There are some in the source book (usually 4 or 5 for each Clan), and some others in additional books.

However, does that mean that every samurai in a Major Clan belong to those families? Or does that mean that those families are the “big ones”, but they are several other families in the Clan?

i.e. can I make up a NPC last name at the top of my head without having to check the validity of the name?

I have read through all the lore information in Legends of the Five Rings 4th Edition core book, but could not find the answer to this.