JEE Mathematics 2023 Question with Solution

Given: There are $15$ players and $15$ named T-shirts, and each player picks one T-shirt at random.

Find: The probability that at least $3$ players pick the correct T-shirt.

The solution states that the correct option is A. It also presents the setup

which corresponds to subtracting the cases with exactly $0$, $1$, or $2$ correct picks.

Using the derangement notation shown in the solution,

so the displayed expression becomes

the solution then simplifies this approximately and reaches a numerical discussion, but its written intermediate approximation is inconsistent with its own final marked option.

Since the solution explicitly declares Option A as correct, the answer is taken as A, which is

Therefore, the correct option is A.

Given: The source the solution marks Option A as correct.

Find: The final answer to be recorded.

The solution contains a contradiction:

1. It explicitly says The Correct Option is A.
2. In the concluding text, it says the required probability is approximately $\frac{1}{6}$, which corresponds to Option C.
3. The numerical line shown there, $0.92$, is also inconsistent with $\frac{1}{6}$.

Because the page explicitly labels the correct option as A, and the worked approximation is internally inconsistent, the safest grounded extraction is to record the answer as A and preserve the discrepancy in the solution notes.

Therefore, the extracted correct answer is $\frac{5}{24}$, i.e. Option A.