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# quiz4solution - SOLUTlO/V Math 125-002 Fall 2009 Quiz 4...

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Unformatted text preview: SOLUTlO/V Math 125-002 Fall 2009 Quiz 4 Name: Last... First... (1) (a) (2 points) How many different plate numbers can be composed if a plate number must consist of two letters followed by three digits? Zé-Zé-IOWOWO (b) (2 points) Same as “a”, but the letters can’t be repeated. 26 - 25-1040- \0 (2) (2 points) Prove that in any group of 110 people, one can ﬁnd ﬁve people whose last names begin with the same letter. “0 objects (?£=7°’€4\ luM-S’l- @L (3-6qu in, 2Q f'boxe_§‘i Hard: {um-rs 04 m {asi- ij * ‘- 1 {e W LL9- ‘: : .— Bb Pkacaﬁ‘HGQ PFLHL Y J T 2.3—1 r4... (MM—Il 5- 9 4W “Mes" MMus 3§¢bjed5 (3) (4 points) Prove that in any group of ten people, there are two people who have the same number of friends in this group. (Assume that the relation “to be a ﬁiend” is symmetric.) For taut (>12;qu Has W)+k& W 444-th 15 in We. m3 0_ q. Case’f No 0% («as q {it-(ends _ Tim we: Lea/c ‘0 wast-+5 (We) a q 6mg (0—- a) sz game 2M q grep/Km. ﬁn ham 1445 0 -Frcema(\$ tau-.41 (“We («we 10 obJ‘ﬁC‘l) in ‘l éoxcs (I— q)_ is 6.0. Cases We haw/e were 066019 Hum Igo’xe) _ B3 P834914- LL14 [urinal-”j W ”I‘m ﬂaw waif W». 2 Zabjedﬁ ...
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