91Ó°ÊÓ

How many permutations are there of the letters in the words (a) TRISKAIDEKAPHOBIA (fear of the number 13\()\) ? (b) FLOCCINAUCINIHILIPILIFICATION (estimating something as worthless)? (c) PNEUMONOULTRAMICROSCOPICSILICOVOLCANOCONIOSIS (a lung disease caused by inhaling fine particles of silica)? (This word is, by some accounts, the longest word in the English language.) (d) DERMATOGLYPHICS (skin patterns or the study of them)? (This word is the (current) longest word in the English language that doesn't repeat a letter; another word of the same length is UNCOPYRIGHTABLE. \(^{13}\) )

Consider an 9 -by- 9 board and nine rooks of which five are red and four are blue. Suppose you place the rooks on the board in nonattacking positions at random. What is the probability that the red rooks are in rows \(1,3,5,7,9 ?\) What is the probability that the red rooks are both in rows \(1,2,3,4,5\) and in columns \(1,2,3,4,5 ?\)

Suppose a poker hand contains seven cards rather than five. Compute the probabilities of the following poker hands: (a) a seven-card straight (b) four cards of one rank and three of a different rank (c) three cards of one rank and two cards of each of two different ranks (d) two cards of each of three different ranks, and a card of a fourth rank (e) three cards of one rank and four cards of each of four different ranks (f) seven cards each of different rank

Four (standard) dice (cubes with \(1,2,3,4,5,6\), respectively, dots on their six faces), each of a different color, are tossed, each landing with one of its faces up, thereby showing a number of dots. Determine the following probabilities: (a) The probability that the total number of dots shown is 6 (b) The probability that at most two of the dice show exactly one dot (c) The probability that each die shows at least two dots (d) The probability that the four numbers of dots shown are all different. (e) The probability that there are exactly two different numbers of dots shown