Solution:
\(\small \text{There are } \dbinom{16}{4} = 1820 \text{ sets of 4-cards. Four of these sets contain exactly one (1) card with a one.}\\ \text {Probability: } \dfrac{4}{1820} = \dfrac{1}{455}\\\)
GA
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I’m leaving this train wreck of a solution here as a sign post to slow down the trains of thought, before changing tracks.
I initially solved this using (4^4) as the number of arrangements where the “1 cards” could occupy any row in the four columns of four rows (this is easy to see). Then dividing this by the total number of combinations,(44) / (nCr(16,4)), gives (64/445) = 0.1406593406593407, the probability.
For some reason, I thought this was too high of a probability....
So, what did I do to “fix” it? I’m not sure ... took the fourth root before dividing it (maybe –IDFK). After changing tracks, I didn’t realize the train actually jumped the tracks until the caboose ended up where the engine should be. This is a simple, high school level probability problem that my cat could solve when buzzed on catnip, yet I turned it into a bloody train wreck.
I am a much better troll than I am a mathematician.
Melody’s solution is defined and nuanced at every step. It’s even better than my cat could do.
GA