different book. mw many different ways arthece earrange lal rapettiona of lotter

Question

different book. mw many different ways arthece earrange lal rapettiona of lotters are NOT al1owed? ) tbi repatitions of Jottera ArE allowed? ot 3 eruste and 10 toppings rvst and exactly 2 tolping# llow many differant pizza5 11e 4 in bow many waya can 20 studenta be assigned to two faculty atudents and tor oach queation. How many diffarent vaya are thare to aver the entire cest S, 5. A multiple choico test consiata of 10 gu.. t i on, with 4 ehoices A coin is tossed D Lines. What is the probability of obtaini 170) 7. Four cards are deait at zandon from a atandard 1101 7 Four cards are dealt at randon deck of 52 carda ot 52 carda. hat is the probability that thero are tuo r black cards? rda and tvo 1. p(A) 0.64 ,,P(B) 0.32, and p(Ann) 0.16, calculate tha en G tollowing probabllitses " 9. Given P(A) 0.5, P(D) probabilitiea 0.6, and p(AID) 0"4, calculate thn " olI gking the Roliing Acrea tlousing Developsent, 420 of the houses have both a deck and a gara prebabtiity that tuch a house has a garage, given that it haa a ns n. auppose that ot all cars on the road have defective brakes 5 cars ase stopeed and inapacted by the state police, compute t at least one of the 5 will have defective

Explanation / Answer

Question 1 :

n = number of different book =8

Total number of arrangentment of 8 dfifferent books arranged in a shelf

( We use permutation n different object taken r at time npr = n! /(n-r)! )

= 8P8 = 8! = 40320

Question 2 :

Number of different letters = 6 ( a,b,c,d,e,f)

Total Number of 4-letters word

i) Repitition is not allowed.

Total Number of 4-letters word = Permutation of 6 letters 4 at time

= 6P4 = 6!/2! = 720/2 = 360

ii) If repetition is allowed

Total Number of 4-letters word = n4 ( use permutation with repetition)

= 64

= 1296

Question 3:

Type of crust = 3 and Type of loppingo = 10

Number of different order of pizza which include 1 type of crust and exactly 2 type loppingo

= 3C1 *10C2 ( We used combination of 'n' different take 'r' at a time)

= 3 * 45

= 135

Question 4 :

n = number of student =20

no. of ways to assign 12 student to A faculty and 8 students to faculty B

= ( First assign 12 student out of 20 student to faculty A and remaining 8 student to faculty B) or (  First assign 8 student out of 20 student to faculty B and remaining 12 student to faculty A )

First assign 12 student out of 20 student to faculty A = 20C12 = 125970 ways

and  remaining 8 student to faculty B = 1 ways

First assign 8 student out of 20 student to faculty B = 20C8= 125970 ways

remaining 12 student to faculty A = 1 ways.

Total number of different ways to assign 12 students to faculty A and 8 student to faculty B

= 125970 +125970

= 251940

Question 5 :

Each question have 4 choices

Hence number of diffrent ways to answer all the question = 104

= 10000

Question 6:

P( getting head) =1/2

n = number of times coins are tossed = 8

X denotes the number of head in 8 tosses

X ~ Bin(n=8,p=1/2)

P( Exactly 4 heads and 4 tails ) = P(X=4)

= 8C4 * (1/2)4 * (1/2)4

= 70 * 1/16 * 1/16

= 70/256

= 0.2734

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