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Permutation and CombinationQuestion and Answers: Page 20

Question Number 49034    Answers: 1   Comments: 0

Question Number 48341    Answers: 0   Comments: 0

Question Number 47656    Answers: 1   Comments: 1

A square is divided into 9 identical smaller squares.Six identical balls are to be placed in these smaller squares such that each of the three rows gets at least one ball(one ball in one square only).In how many different ways can this be done? a)91 b)51 c)81 d)41

$${A}\:{square}\:{is}\:{divided}\:{into}\:\mathrm{9}\:{identical} \\ $$$${smaller}\:{squares}.{Six}\:{identical}\:{balls} \\ $$$${are}\:{to}\:{be}\:{placed}\:{in}\:{these}\:{smaller}\: \\ $$$${squares}\:{such}\:{that}\:{each}\:{of}\:{the}\:{three} \\ $$$${rows}\:{gets}\:{at}\:{least}\:{one}\:{ball}\left({one}\right. \\ $$$$\left.{ball}\:{in}\:{one}\:{square}\:{only}\right).{In}\:{how} \\ $$$${many}\:{different}\:{ways}\:{can}\:{this}\:{be} \\ $$$${done}? \\ $$$$\left.{a}\left.\right)\left.\mathrm{9}\left.\mathrm{1}\:{b}\right)\mathrm{51}\:{c}\right)\mathrm{81}\:{d}\right)\mathrm{41} \\ $$$$ \\ $$

Question Number 46143    Answers: 1   Comments: 0

Question Number 43824    Answers: 1   Comments: 0

Question Number 43659    Answers: 1   Comments: 2

An unfair coin with the probability of getting head in one toss = (1/5). If coin tosses n times, the probability of getting 2 heads is equal to the probability of getting 3 heads. Find n

$$\mathrm{An}\:\mathrm{unfair}\:\mathrm{coin}\:\mathrm{with}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{getting} \\ $$$$\mathrm{head}\:\mathrm{in}\:\mathrm{one}\:\mathrm{toss}\:=\:\frac{\mathrm{1}}{\mathrm{5}}. \\ $$$$\mathrm{If}\:\mathrm{coin}\:\mathrm{tosses}\:{n}\:\mathrm{times},\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{getting}\:\mathrm{2}\:\mathrm{heads}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\: \\ $$$$\mathrm{getting}\:\mathrm{3}\:\mathrm{heads}.\:\mathrm{Find}\:{n} \\ $$

Question Number 43343    Answers: 1   Comments: 0

how many odd numbers greater than 60000 can be made from the digits 5,6,7,8,9,0 if no number contains any digit more than once?

$$\mathrm{how}\:\mathrm{many}\:\mathrm{odd}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{60000}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{0}\:\mathrm{if}\:\mathrm{no}\:\mathrm{number}\:\mathrm{contains} \\ $$$$\mathrm{any}\:\mathrm{digit}\:\mathrm{more}\:\mathrm{than}\:\mathrm{once}? \\ $$

Question Number 43031    Answers: 2   Comments: 2

Question Number 42494    Answers: 1   Comments: 1

In the sequence of numbers 1, 2, 11, 22, 111, 222, ... the sum of the digits in 999th terms is ??

$$\mathrm{In}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{numbers}\:\:\mathrm{1},\:\mathrm{2},\:\mathrm{11},\:\mathrm{22},\:\mathrm{111},\:\mathrm{222},\:...\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits} \\ $$$$\mathrm{in}\:\mathrm{999th}\:\mathrm{terms}\:\mathrm{is}\:?? \\ $$

Question Number 42332    Answers: 0   Comments: 0

Question Number 42110    Answers: 1   Comments: 1

Question Number 42107    Answers: 0   Comments: 0

Question Number 42106    Answers: 1   Comments: 0

Question Number 41824    Answers: 3   Comments: 0

if ^n C_5 = ^n C_(11) find ^(18) C_n

$$\mathrm{if}\:\:\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{5}} \:=\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{11}} \:\:\:\mathrm{find}\:\:\:\:\:\:\overset{\mathrm{18}} {\:}\mathrm{C}_{\mathrm{n}} \\ $$

Question Number 40550    Answers: 1   Comments: 0

if three numbers are drawn at random successively without replacement from a set S={1,2,......10}then probability that the minimum of the choosen number is 3 or their maximum is 7 Answer=((11)/(40))

$$\mathrm{if}\:\mathrm{three}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{at}\:\mathrm{random} \\ $$$$\mathrm{successively}\:\mathrm{without}\:\mathrm{replacement}\:\mathrm{from} \\ $$$$\mathrm{a}\:\mathrm{set}\:\mathrm{S}=\left\{\mathrm{1},\mathrm{2},......\mathrm{10}\right\}\mathrm{then}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{choosen}\:\mathrm{number}\:\mathrm{is} \\ $$$$\mathrm{3}\:\mathrm{or}\:\mathrm{their}\:\mathrm{maximum}\:\mathrm{is}\:\mathrm{7}\:\:\:\:\:\:\:\: \\ $$$$\:\mathrm{Answer}=\frac{\mathrm{11}}{\mathrm{40}} \\ $$

Question Number 40216    Answers: 1   Comments: 0

Question Number 39846    Answers: 2   Comments: 2

the sum of the four digit even numbers that can be formed with digits 0 3 5 4 without repitation

$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{four}\:\:\mathrm{digit}\:\mathrm{even}\:\mathrm{numbers}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{with}\:\mathrm{digits}\:\mathrm{0}\:\mathrm{3}\:\mathrm{5}\:\mathrm{4}\:\mathrm{without}\:\mathrm{repitation} \\ $$

Question Number 37648    Answers: 1   Comments: 0

A particle, of mass 5kg,moves in a straight line its displacement,x metres after t seconds is given by x = t^3 − 4t^2 +4t. Find the magnitude of the impulses exerted on the particle when t=2.

$$\mathrm{A}\:\mathrm{particle},\:\mathrm{of}\:\mathrm{mass}\:\mathrm{5kg},\mathrm{moves}\:\mathrm{in} \\ $$$$\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{its}\:\mathrm{displacement},\mathrm{x} \\ $$$$\mathrm{metres}\:\mathrm{after}\:\mathrm{t}\:\mathrm{seconds}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$${x}\:=\:{t}^{\mathrm{3}} −\:\mathrm{4}{t}^{\mathrm{2}} +\mathrm{4}{t}.\:{F}\mathrm{ind}\:\:\mathrm{the}\:\mathrm{magnitude} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{impulses}\:\mathrm{exerted}\:\mathrm{on}\:\mathrm{the}\:\mathrm{particle} \\ $$$$\mathrm{when}\:\mathrm{t}=\mathrm{2}. \\ $$

Question Number 36784    Answers: 0   Comments: 0

Prove that Σ_(r=0) ^n r ((n),(r) )^2 = n (((2n − 1)),(( n − 1)) )

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{r}\:\begin{pmatrix}{{n}}\\{{r}}\end{pmatrix}^{\mathrm{2}} \:=\:{n}\:\begin{pmatrix}{\mathrm{2}{n}\:−\:\mathrm{1}}\\{\:\:{n}\:−\:\mathrm{1}}\end{pmatrix} \\ $$

Question Number 36398    Answers: 1   Comments: 1

Consider triangle ABC.If 206 lines are drawn from A to BC how many triangles are formed?

$${Consider}\:{triangle}\:{ABC}.{If}\:\mathrm{206} \\ $$$${lines}\:{are}\:{drawn}\:{from}\:{A}\:{to}\:{BC}\:{how} \\ $$$${many}\:{triangles}\:{are}\:{formed}? \\ $$

Question Number 35640    Answers: 1   Comments: 0

A panel of 3 women and 4 men is to be formed from 8 women and 7 men.Find the number of ways which the panel can be formed if it must contain at least 2 women.

$${A}\:{panel}\:{of}\:\mathrm{3}\:{women}\:{and}\:\mathrm{4}\:{men}\:{is} \\ $$$${to}\:{be}\:{formed}\:{from}\:\mathrm{8}\:{women}\:{and} \\ $$$$\mathrm{7}\:{men}.{Find}\:{the}\:{number}\:{of}\:{ways} \\ $$$${which}\:{the}\:{panel}\:{can}\:{be}\:{formed}\:{if} \\ $$$${it}\:{must}\:{contain}\:{at}\:{least}\:\mathrm{2}\:{women}. \\ $$

Question Number 35639    Answers: 0   Comments: 1

Three boys,two girls and a puppy sit at a round table.In how many ways can they be arranged if the puppy is to be seated i)between the two girls ii)between any two boys

$${Three}\:{boys},{two}\:{girls}\:{and}\:{a}\:{puppy} \\ $$$${sit}\:{at}\:{a}\:{round}\:{table}.{In}\:{how}\:{many} \\ $$$${ways}\:{can}\:{they}\:{be}\:{arranged}\:{if}\:{the} \\ $$$${puppy}\:{is}\:{to}\:{be}\:{seated} \\ $$$$\left.{i}\right){between}\:{the}\:{two}\:{girls} \\ $$$$\left.{ii}\right){between}\:{any}\:{two}\:{boys} \\ $$

Question Number 35348    Answers: 0   Comments: 0

Question Number 35347    Answers: 3   Comments: 0

Question Number 35344    Answers: 0   Comments: 0

Question Number 35165    Answers: 0   Comments: 2

In how many ways can a committee of 11 people be selected from 9 people.

$${In}\:{how}\:{many}\:{ways}\:{can}\:{a}\:{committee} \\ $$$${of}\:\mathrm{11}\:{people}\:{be}\:{selected}\:{from}\:\mathrm{9} \\ $$$${people}. \\ $$

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