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If I have $1$ jar of $20$ balls with $10$ red, $5$ blue and $5$ yellow, $1$ jar of $30$ balls with $10$ red, $10$ blue and $10$ yellow and $1$ jar of $50$ balls with $15$ red, $20$ blue and $15$ yellow, but I can only pick three from each jar without replacement. How many events occur where there is the colour of the ball in the same position across the three jar selections, excluding events where there are multiple balls that are in the same position and colour across all three selections?

Situation as shown in this rough sketch

For Example: Jar 1:(Red, Blue, Red) Jar 2:(Yellow, Blue, Red) Jar 3:(Blue, Blue, Blue), this would be an even where a blue ball has been selected in the same position across all three jars.

Another Example: Jar 1:(Red, Blue, Red) Jar 2:(Yellow, Blue, Red) Jar 3:(Blue, Blue, Red), this would be an even where a blue ball and a red ball has been selected in the same position across all three jars and is excluded from the answer to the problem.

NAZBOL
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  • So to be clear, you just want to find the number of situations where exactly one colour was drawn from all three jars, and the other colours were not drawn from all three jars? – Jack Crawford May 21 '19 at 02:29
  • Also @NAZBOL welcome to Math.SE comrade, but please do not do this thing where you ask essentially the same question three times (https://math.stackexchange.com/q/3233614/675062) — since the solution to this part of the question could quite possibly depend on the solution to the part preceding it, it’s probably better if they’re in the same thread! You can ask multiple sub-parts of a question in the same post. The names you gave the questions also probably don’t illuminate what is actually being asked precisely enough (since you have each the exact same title with a different number). – Jack Crawford May 21 '19 at 02:34
  • @JackCrawford I want to find the number of situations where only one colour of ball was drawn in the same position from all three jars, while the other two selections of balls are not the same colour of ball in the same position as the other two jars. So, I couldn't have (blue, blue, blue) (blue, blue, blue) (blue, blue, blue) either, just one ball that shares the same colour and position out of the three balls selected. – NAZBOL May 21 '19 at 02:39
  • @JackCrawford Thankyou for informing me of my mistake. I'll be careful to not repeat it in the future. – NAZBOL May 21 '19 at 02:40
  • also related: https://math.stackexchange.com/questions/3232893/permutations-of-alike-objects – Henry May 21 '19 at 16:17

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