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

Question

The probability that three cards drawn from a pack of 52 cards, all are red is (A) (1/17) (B) (4/17) (C) (3/17) (D) (2/17)

Tardigrade Admin · Accepted Answer

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}

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