MHT CET · Maths · Probability

The probability that three cards drawn from a pack of 52 cards, all are red is

A $\frac{1}{17}$
B $\frac{4}{17}$
C $\frac{3}{17}$
D $\frac{2}{17}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{2}{17}$

Step-by-step Solution

Detailed explanation

Total number of ways that three card drawn from a pack of 52 cards are

^{52} C_{3}

and number of ways that three red. cards drawn are

^{26} C_{3}

.
Required probability

= \frac{^{26} C_{3}}{^{52} C_{3}} = \frac{26 \times 25 \times 24}{52 \times 51 \times 50}

= \frac{2}{17}

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.

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