This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: SOLUT/O/V Math 125002 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: (CHClk) 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"Elizgl=l_£l,rv\M—l :5 TLZIewﬁ 6:] ﬁktm‘ LVCL FL‘C’LP‘Q «aw; law we cm \ch Swm F762 'w‘cVx @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. Lelc 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 :(8mlT/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 =LtS3':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)—... éS‘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 twoorthree 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 6letter 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.) 106149 (10) How many different words (not necessarily real vocabulary words)
can be composed using 5 letters a and 3 letters b? Lettears 6?. Mg m 0W3 5 FQHWS
I‘m My geé/He/r Word. 30 no) ...
View
Full Document
 Fall '08
 Staff
 Math

Click to edit the document details