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Unformatted text preview:Math325 Test 1 (on 2.1 to 2.6, 3.1, 3.2, 5.1, 5.2, 5.4, 5.5)
No calculators! Show your work! Total time: 50 minutes. Total points: 100 1'. , (14 pts) How many even numbers between 100,000 and 900,000 (inclusive) have distinct
digits? Express your answer as a product of one-digit number. W Mir/(52 @Mm nW/C/r 4'00) an?) MS pom/5.
"ma "4% 2 Qua-m, VLLVH/"M MUM/W [06?) (719.0 ﬁnd/1 027,672 ) _
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6M 2: (f A64? is 2] 4/ ) [5+ L6, ti ff»? 3 WT) 1m deans it, M&JI\T1 — 2. 14pts) Howmany distinct 6-tter 'wod' (nOt necesarily real words) can be formed
from 3 A's, 2 B's, and a C? Express your answer as a number. 'ﬂm parmwfmﬁém/ em Why/f" (3A , 243, mg .
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"Q! 2" .S/FX 6/5 -\ m... so wmmwmﬁwﬂwwamxwn_,__4, mammal, MW A, 3. (14pts) How many 20-combinations of the multiset {oo - a,oo -b,oo - c,oo - d} are there such that a gets chosen at least once, 1) gets chosen at least twice, c gets chosen at least three
times, and d gets chosen at least four times? Express your answer in terms of factorials. [~tZ+3+4}—:lv, lowsla : [a 4. (16pts) Use the pigeonhole principleto show that if 11 integers are chosen from the set
{1, 2, ..., 20}, then the selection includes integers a and b such that a —— b = 2 . (hint:
partition the set into 10 subsets (10 pigeonholes) of cardinality 2) . {I/Z J n.) W'Wﬂ (c2 19%ng L, t"? W of 'm "We,
at 1660* M Wt Mix/WW .2 {Meg/M a, b ,2 Cl ~'o Q 2— WMWLW' 5. (14pts) Evaluate 2(4)" 4" . Write your answer in exponential form.
V =0 , (l) W" I" , i In
:2 (44%)" 2' l" )1 6. (14pts) Whatis the coefﬁcient of u3v2t in the expansion of (t — 2u + 4v)6 ? Express your
answer as a number. V l' ﬁlial/Q +904: <5 2) t (~zu)3(qxu 3" Wﬁwm : <1 1351)? #71 1: 6" #8) C16) 2.! \. 7. (14pts) Use Newton's binomial theorem to approximate W . Write your answer in terms 0 ani 1ni e series. 0( 0o ,
f_nft {VH2} :% 96C)8k \' 1 "x 3 a... ' . 2'6 " 15 ' (17'03 '2 law will 3 i N _l
sweep/3: 3 21;; be)" 2. ) 'éyé'xr'ri '(Ie' :2 76870
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