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STAT 511 Counting Handout

1. The population of a town is 20,000. If each resident has three initials, is it truethat at least two people have the sae initials! "#plain.

2. $o% has nine guests to his house, two of which are &ane and 'ind(. If the guests

arrive in rando order, what is the pro%a%ilit( that)

&ane will not arrive right after 'ind(!

&ane arrives %efore 'ind( and at least * people arrive %etween the!

+. ne of the elevators in the 'ath %uilding starts with * people and stops at -floors. Assuing it is euall( li/el( that a passenger gets off at an( of these -

floors, what is the pro%a%ilit( that)

no%od( gets off on the thor -thfloor!

at least two passengers get off on the sae floor!

. In how an( different wa(s can 1* offices %e painted if)

each office is paint with one of four different colors!

each of four different colors is used e#actl( ties!

5. ive different nu%ers are chosen at rando fro 0 to 33. 4hat is thepro%a%ilit( that)

all five nu%ers selected are odd!

the nu%er - is chosen!

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ptional)

*. How an( eight digit nu%ers are there without two identical nu%ers ne#t toeach other!

. A ultiple choice test has 20 uestions, each having five possi%le answers. "ach

uestion has onl( one correct answer. If the uestions are answered at rando,what is the pro%a%ilit( of getting)

all of the right!

at least 1- right!

-. Suppose 1 arried couples ta/e part in a contest. ourteen identical pries are

given to 1 different individuals, with each person having an eual chance of

winning one of the pries. 4hat is the pro%a%ilit( that)

one person in each couple wins a prie!

e#actl( couples win all 1 pries!

3. In a closet there are - pairs of shoes. Si# shoes are selected at rando. 4hat isthe pro%a%ilit( of getting)

no atching pairs!

onl( one pair of atching shoes!

two pairs of atching shoes!

three pairs of atching shoes!