Question

A deck contains 13 cards numbered 1 through 13. What is the probability that the first five cards in the deck are all bigger than 8? (Assume that all possible

orderings of the cards are equally likely.)

Answer 1

The first card drawn can be any number among 9, 10, 11, 12, or 13. There are five possible cards greater than 8.

Therefore,

number of possibilities for first card =5.

Similarly, for second card, there are four possibilities since one card is already drawn.

number of possibilities for second card = 4.

Similarly for third, fourth and fifth draw, we have 3, 2 and 1 possibilities (for greater than 8).