Lecture Hall A lecture hall has five doors. In how many ways can a student enter the hall by one door and (a) Exit by a different door? (b) Exit by any door? Poker Hand A poker hand consists of 5...

Lecture Hall A lecture hall has five doors. In how many ways can a student enter the hall by one door and

(a) Exit by a different door?

(b) Exit by any door?

Poker Hand A poker hand consists of 5 cards drawn from a deck of 52 playing cards. The hand is said to be “four of a kind” if four of the cards have the same face value. For example, hands with four 10’s or four jacks or four 2’s are four-of-a-kind hands. How many such hands are possible?