Math 1113 Week 7 PDF

Permutat on Comb nat on and Probal ty some event Econ occur n ple n n and second event F can...

Permutat on Comb nat on and Probal ty some event Econ occur n ple n n and second event F can occur n ways ways s multaneously Suppose that both event can not occur F can occur n Mtn Then E and ways there s an 1 Product Rule Pr nc ple Suppose that s an there event E wh ch can occur n n ways Then the comb nat on n a event F wh ch can occur ways F occur n m n ways E and can of In another words Mat Mat tn ways at the same t me no two events occur f My 12 Mr ways event another f one occur after courses 4 d ffer E A college has d fferent h story 3 curses l terature and 2 d fferent soc ology a student can choose F nd the number a each k nd ways of one of courses of student can choose b F nd the number ways a  y of the courses just one soc ology 3 2 I 24 d fferent ways 3 4 2 9 d fferent cho ces ne pos t ve ntegers from denoted and to a s def ned as n factor al n by 1 1.2 ___ G 1 n Fe example 5 1.2.3.415 120 A 1 1 1 Mostfrequently use dent ty N n n.cn 1 A 1 1 1 2 A 3 n.CA 1 G 2  A 1 1 G rt11 CA rt n.cn 1 Artı 2 D and hand s de ayn Cons der RHS r ght of d v de t r by EE.EE BÜYÜTEÇ arenas a pos t ve as ntegers w th en s def ned 1 II For example 15 12 9 41 9 71 4 12  result that obta n general ze the we INE can and a ex from 7 1hr other words atb n then a n f 1 IJT.genentyfsetof. n objects n order s called a permutat on g ven these objects Any arrangement of any ran of n order s called g venr permutat on at n objects taken or a t me a permutat on of PCnr and It denoted s by IPCn rl n.mn A real f  F nd the number three letter_word Example the letters A B C DE w thout referof us ng 6 5 120 120 P 6,31 f 3 6 5.4 6 letter words 6 of 6 4 2 1 6 716.6 Ğü üE mult et of a deal w th the number of We permutat ons wh ch are al ke that s a set of objects some of P n nn na n of n objects of denotes wh ch the number An are al ke of permutat on ne are al ke n are al ke Planı a n.IT  Cons der the word BABBY F nd the Example number all poss ble 5 letter words of B B B AY B B B AY words all the same AYYy are B2 B B Ba Ba B AY Bo Be BAY Ba BaB AY 20 words P 5 3 1 F nd the number seven letter words that Ed the letters of BE 2E.IE can be formed us ng of P 7 3,2 1 1 420 words poss ble d fferent Comb nat ons elements A comb nat on set Let S be elements a taken of r at a t me s any of n element küçük of select on r count Such select on s called r_comb nat on It s S w th r elements s mply number subsets of  y denoted Cla r and by comb nat ons 4 objects Iy F nd the number of of D taken 0 at a t me AB C ACB BAC BCA CAB CBA AB C ABC BDA DAB DBA AB D ABD ADB BAD CDA DAC DCA CD A CD ADC CAD BBC DCB BCD BCD BBC CBD CDB P 4 3 3 43 1 0 164,31 41 Yenn from a AmyIpgG man who has 6 cows 5 p gs ch ckens and 8 number cho ces that theformer ch ckens F nd the The cho ces sous 6,31 G 20 of 3 31 The cho ces ofp gs 512 5 10  The cho ces ch ckens 8,4 70 of The number all poss ble shoes s of 20 10.70 140004 9 52 ˢ.ec İ ĞÜE edynnp gen s then at least one p geonhole or more p geons more than one p geon occup ed by nvolve 13 person Let of fr ends born n the same E a group at least two them was Then month of December III III class to be F nd the number students n a Es them were born n the three sure that of same month 2 12 We have 12 p geonhole here We went 3 of them were bornsönük II students m numum s by  g n.lk 1 1 students number F nd the m n mum them belong to the of Eggs varantee that 5 Freshman of Sophomore Jun or Sen or same class of 1ˢᵗgrade 3 grade 4ᵗʰgrade 42ⁿᵈgradel p geonhole 4 of5 5 them need to be n the class of M n mum students 4 5 1 1 174 of