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Home » Shorter Is Hotter: Perfect Short Curly Hairstyles for Modern Men! - jntua results

Shorter Is Hotter: Perfect Short Curly Hairstyles for Modern Men! - jntua results

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 5Question: A cognitive scientist is analyzing decision-making strategies in which participants choose between four equally likely options. If a participant selects one option at random each time and makes exactly four independent choices, what is the probability that exactly two of the chosen options are the same and the other two are each different from each other and from the repeated one?

📌 We are to compute the probability that in 4 independent choices among 4 options (say labeled A, B, C, D, with equal likelihood), exactly one option appears twice, and two other distinct options appear once each, with the fourth position filled by a fourth distinct option — but wait: this would require 4 distinct options total, and one repeated. Since only 4 positions exist, and we want exactly one option repeated, and the other two being different, the only valid pattern is: one option appears twice, two others appear once, and the fourth option appears zero times — but that’s only 4 choices total. So the pattern is: one option repeated twice, and two other distinct options appearing once each — that uses up 2 + 1 + 1 = 4 choices, with one option appearing twice and two others once each, and one option not used at all. So the multiset of choices is of the form {A, A, B, C}, where A, B, C are distinct, and D is unused.

📌 We compute the probability of such a multiplicity pattern.

📌 Total number of possible outcome sequences: $4^4 = 256$, since each of the 4 decisions has 4 choices.

📌 Now count favorable outcomes.

📌 Step 1: Choose the option that appears twice: $\binom{4}{1} = 4$ ways.

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