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Permutation and CombinationQuestion and Answers: Page 1

Question Number 205683    Answers: 1   Comments: 0

$$\:\:\:\:\: \\ $$

Question Number 205690    Answers: 0   Comments: 3

Question Number 205045    Answers: 0   Comments: 4

$$\:\:\:\:\underbrace{ \underline{}\:} \\ $$

Question Number 203833    Answers: 1   Comments: 0

How many bit strings of length 11 have exactly three consecutive 1s?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{bit}\:\mathrm{strings}\:\mathrm{of}\:\mathrm{length}\:\mathrm{11}\:\mathrm{have} \\ $$$$\mathrm{exactly}\:\mathrm{three}\:\mathrm{consecutive}\:\mathrm{1s}? \\ $$

Question Number 203832    Answers: 2   Comments: 0

How many bit strings of length 10 do not have four consecutive 1s?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{bit}\:\mathrm{strings}\:\mathrm{of}\:\mathrm{length}\:\mathrm{10}\:\mathrm{do}\:\mathrm{not} \\ $$$$\mathrm{have}\:\mathrm{four}\:\mathrm{consecutive}\:\mathrm{1s}? \\ $$

Question Number 203198    Answers: 0   Comments: 0

Question Number 202598    Answers: 2   Comments: 0

Question Number 202584    Answers: 1   Comments: 0

$$\:\:\: \\ $$

Question Number 202374    Answers: 1   Comments: 2

Question Number 202257    Answers: 0   Comments: 1

Question Number 201839    Answers: 0   Comments: 1

Question Number 200051    Answers: 2   Comments: 2

There are many ways to arrange 3 red balls and 9 black balls in a circle so that there are a minimum of 2 black balls between 2 adjacent red balls. (a) 180×8! (b) 240×7! (c) 364×6! (d) 282×4! (e) 144×5!

$$ \\ $$$$\mathrm{There}\:\mathrm{are}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{arrange}\:\mathrm{3}\:\mathrm{red} \\ $$$$\:\mathrm{balls}\:\mathrm{and}\:\mathrm{9}\:\mathrm{black}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\: \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{a}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{2} \\ $$$$\mathrm{black}\:\mathrm{balls}\:\mathrm{between}\:\mathrm{2}\:\mathrm{adjacent}\:\mathrm{red} \\ $$$$\mathrm{balls}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{180}×\mathrm{8}!\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{240}×\mathrm{7}!\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{364}×\mathrm{6}! \\ $$$$\:\left(\mathrm{d}\right)\:\mathrm{282}×\mathrm{4}!\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{144}×\mathrm{5}!\: \\ $$

Question Number 199337    Answers: 1   Comments: 0

Question Number 199333    Answers: 2   Comments: 0

Find the number of integers greater than 6200 that can be formed from the digits 1,3,6,8 and 9, where each digit is used at most once.

$${Find}\:{the}\:{number}\:{of}\:{integers}\:{greater} \\ $$$${than}\:\mathrm{6200}\:{that}\:{can}\:{be}\:{formed}\:{from} \\ $$$${the}\:{digits}\:\mathrm{1},\mathrm{3},\mathrm{6},\mathrm{8}\:{and}\:\mathrm{9},\:{where}\:{each} \\ $$$${digit}\:{is}\:{used}\:{at}\:{most}\:{once}. \\ $$

Question Number 199270    Answers: 2   Comments: 4

Question Number 199353    Answers: 0   Comments: 4

What is the probability that in a class of 18 people, there exists exactly a group of exactly 3 people born on the same day of the week?

$${What}\:{is}\:{the}\:{probability}\:{that}\:{in}\:{a}\:{class}\: \\ $$$${of}\:\mathrm{18}\:{people},\:{there}\:{exists}\:{exactly}\:{a}\: \\ $$$${group}\:{of}\:{exactly}\:\mathrm{3}\:{people}\:{born}\:{on}\:{the} \\ $$$${same}\:{day}\:{of}\:{the}\:{week}? \\ $$

Question Number 199054    Answers: 2   Comments: 0

x

$$\:\:\boldsymbol{{x}} \\ $$

Question Number 199031    Answers: 1   Comments: 0

Question Number 198851    Answers: 1   Comments: 12

You want to arrange 17 books on the shelf of a bookstore. The shelf is dedicated to the three Toni Morrison novels published between 1977 and 1987: Song of Solomon, Tar Baby, and Beloved. You have many copies of each, but on the shelf you want an even number of Song of Solomon, at least three copies of Tar Baby, and at most four copies of Beloved. How many different arrangements are possible?

You want to arrange 17 books on the shelf of a bookstore. The shelf is dedicated to the three Toni Morrison novels published between 1977 and 1987: Song of Solomon, Tar Baby, and Beloved. You have many copies of each, but on the shelf you want an even number of Song of Solomon, at least three copies of Tar Baby, and at most four copies of Beloved. How many different arrangements are possible?

Question Number 198809    Answers: 2   Comments: 0

sum of roots log _3 x + log _3 (2,5) + log _x 9 = 3+ log _x 5

$$\:\:\:\:\:{sum}\:{of}\:{roots}\: \\ $$$$\:\mathrm{log}\:_{\mathrm{3}} {x}\:+\:\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{2},\mathrm{5}\right)\:+\:\mathrm{log}\:_{{x}} \mathrm{9}\:=\:\mathrm{3}+\:\mathrm{log}\:_{{x}} \mathrm{5}\: \\ $$

Question Number 198576    Answers: 1   Comments: 10

How many numbers with a maximum of 5 digits, greater than 4000, can be formed with the digits 2, 3, 4, 5, 6; if repetition is allowed for 2 and 3 only?

How many numbers with a maximum of 5 digits, greater than 4000, can be formed with the digits 2, 3, 4, 5, 6; if repetition is allowed for 2 and 3 only?

Question Number 198242    Answers: 1   Comments: 3

How many numbers with a maximum of 5 digits, greater than 4000, can be formed with the digits 2, 3, 4, 5, 6; if repetition is allowed for 2 and 3 only?

How many numbers with a maximum of 5 digits, greater than 4000, can be formed with the digits 2, 3, 4, 5, 6; if repetition is allowed for 2 and 3 only?

Question Number 198231    Answers: 1   Comments: 0

Question Number 198022    Answers: 1   Comments: 0

Five letters are selected from

$$\:\:\mathrm{Five}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{selected}\:\mathrm{from} \\ $$

Question Number 197564    Answers: 1   Comments: 4

sir...number of 3 digit numbers which are divisible by a)3 b)4 c)6 d)7 e)8 f)9 g)11 when repetetion is 1)Allowwd 2)Not allowed.. kindly help me sir

$${sir}...{number}\:{of}\:\mathrm{3}\:{digit} \\ $$$${numbers}\:{which}\:{are}\:{divisible} \\ $$$${by}\: \\ $$$$\left.{a}\left.\right)\left.\mathrm{3}\left.\:\left.\:\left.{b}\left.\right)\mathrm{4}\:\:{c}\right)\mathrm{6}\:\:{d}\right)\mathrm{7}\:\:{e}\right)\mathrm{8}\:\:{f}\right)\mathrm{9}\:\:{g}\right)\mathrm{11} \\ $$$${when}\:{repetetion}\:{is} \\ $$$$\left.\mathrm{1}\left.\right){Allowwd}\:\:\mathrm{2}\right){Not}\:{allowed}.. \\ $$$${kindly}\:{help}\:{me}\:{sir} \\ $$

Question Number 197311    Answers: 1   Comments: 0

Prove that _(n+1) C_r = _n C_r + _n C_(r−1)

$$\:\:\:\:\:\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\:_{\mathrm{n}+\mathrm{1}} \:\mathrm{C}_{\mathrm{r}} \:=\:_{\mathrm{n}} \mathrm{C}_{\mathrm{r}} \:+\:_{\mathrm{n}} \mathrm{C}_{\mathrm{r}−\mathrm{1}} \: \\ $$

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