Suppose five cards are drawn without replacement from a standard 52-card deck and order is irrelevant. Find each of the following.\ a. The probability of drawing a royal flush (ace, king, queen, jack, and 10 of a single suit). b. The probability of drawing a straight flush (A straight flush is any sequence of five cards in a single suit that is NOT a royal flush. Since an ace can count as a 1 in straights, the hand {ace, 2, 3, 4, 5} of a single suit is one example of a straight flush.)

A computer manufacturer knows that, in a box of 175 computer chips, 5 will be defective. Max will draw 2 chips at random, from a box of 175. Determine, to the nearest hundredth, the probability that Max will draw 2 non-defective chips.

Suppose you draw two cards from a standard deck of cards. You do NOT replace the first card. What is the probability of drawing two red cards (e.g. two hearts/two diamonds/one of each)? Assume * means multiplication.

An undergraduate research committee consisting of 4 people is to be formed form 12 doctoral students and 4 supervisors. Find the probability that the committee will consist of exactly 2 doctoral students.