WBJEE · Maths · Probability

A poker hand consists of 5 cards drawn at random from a well-shuffled pack of 52 cards. Then, the probability that a poker hand consists of a pair and a triple of equal face values (for example, 2 sevens and 3 kings or 2 aces and 3 queens, etc. ) is

A \(\frac{6}{4165}\)
B \(\frac{23}{4165}\)
C \(\frac{1797}{4165}\)
D \(\frac{1}{4165}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{6}{4165}\)

Step-by-step Solution

Detailed explanation

Required probability \(\frac{{ }^{13} c_1 \times{ }^4 c_2 \times{ }^{12} c_1 \times{ }^4 c_3}{{ }^{52} c_5}\) \(\frac{13 \times 6 \times 12 \times 4}{\frac{52 \times 51 \times 50 \times 49 \times 48}{5 \times 4 \times 3 \times 2 \times 1}}\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From WBJEE

Explore more questions on app