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# exam2solution - SOLUT/O/V Math 125-002 Fall 2009 Exam 2...

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Unformatted text preview: SOLUT/O/V Math 125-002 Fall 2009 Exam 2 Name: Last... First... Book closed. Calculator and notes may not be used. Each problem is worth 10 points. (1) Solve the recurrence relation an = 6a,...1 — 5on4 given a0 = 2, Ctz—l C123 (2) Solve the recurrence relation on = Gap; — 9a,..2 given as = 2, @213 ah _éau-—k %qak~2:o y2a6\$+q20 Xk=X2—:3 ah: (CH-Clk) 5‘“ kto ﬁc‘ t 2-. \ C‘ﬁ’cz: '5 C3— 4 I! 61.42%? 3‘“ (3) Prove that in any group of 50 people, one can ﬁnd 5 people who have birthdays in the same month. l-"Elizg-l=l_£l,rv\M—l :5- TLZI-ewﬁ 6:] ﬁktm‘ LVCL FL‘C’LP‘Q «aw; law we cm \ch Swm F762 'w‘c-V-x @Irﬂalags 1H W 3% "ll/1 (4) Prove that in any list of twelve natural numbers, one can ﬁnd two numbers whose diﬂ'erence is divisible by 8. Le-lc Q4)...C{~ a.” b: +Lese "Mars. )L’ g ”19,“; (rename). B} P Fri udffe )m Oil- W 60%“ >3, 2 ogjecils) Sexj 1‘; 3 F5 ~ “rem CLLHQJ :(8m-lT/cﬁaC8mr5 3 :: 6(ML—M5j —— oak/:9“? €38. (5) How many natural numbers a: in the interval 1 S w 5 500 are divis- ible by 11 but not divisible by 13? (Sinceslmﬂ? you may not use calculator, the following may help: 1—] =45. 4545..., =38. 4615.. ., % — 3.49...) Pd- :1) -{><l léxssoo and gt.) ouvtgﬁégfjhii 0"" 1311\)13\: ‘D4al“‘D4‘ln D‘J: [D441 DH; Sg—wj— \$2 =LtS-3':LIZ {Kean—1:344“ I} We. PHHS M64 “43"“3 (6) Expand the following expressions (for example, 4! = 4 - 3 - 2 - 1; do not conclude arithmetics.) "Q‘SW‘B‘ZJ 13(63):... g S H (6)—... é-S-‘l 3 _ 3 2- I In problems 7 — 10, you may leave the answer in converted form, for example, 7! + 5, or P(6, 3) - 23, or 5- ( g ) = Do not expand, do not ﬁnish arithmetics. (7) How many two-or-three digit numbers can be composed using only odd digits? Me Me, 5 00M waxes: m, 5,7, ‘7 136 7 :. 55+ 55-? (8) How many different 6-letter words (not necessarily real vocabulary words) can be composed using each of the letters a, b, c, d, e, f exactly once if it is required that letters a and b stand together? Con \$1M PMWVEWS 05f— Save oéed‘y. salt} goneﬁ) Ma Ma W‘ MW“ 3a,bj'g)w &++e4~5 CM ﬁe Pd 0" ‘6‘” 01/38me way} So 3251.2 (9) How many different ways are there to award one ﬁrst mg, one second prjge and three third prices in a. contest of ten peop e? (A contestant may not receive more than one prif.) 10-6149 (10) How many different words (not necessarily real vocabulary words) can be composed using 5 letters a and 3 letters b? Let-tears 6?. Mg m 0W3 5 FQHWS I‘m My geé/He/r Word. 30 no) ...
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