Question and Answers Forum

Permutation and CombinationQuestion and Answers: Page 9

Question Number 134329 Answers: 2 Comments: 0

How many ways can 15 basketball players be assigned to Team A, Team B, and Team C with 5 players on each team?

$$ \\ $$How many ways can 15 basketball players be assigned to Team A, Team B, and Team C with 5 players on each team?

Question Number 134292 Answers: 1 Comments: 0

The digits 1, 2, 3, 4, 5, 6, and 7 are written on separate cards. Three are drawn and placed in order of drawing. In how many ways can numbers greater than 500 be formed?

$$ \\ $$The digits 1, 2, 3, 4, 5, 6, and 7 are written on separate cards. Three are drawn and placed in order of drawing. In how many ways can numbers greater than 500 be formed?

Question Number 134232 Answers: 2 Comments: 0

In how many ways can 5 men, 4 women, and 3 children be arranged in a row of 12 seats if the children sit together?

$$ \\ $$In how many ways can 5 men, 4 women, and 3 children be arranged in a row of 12 seats if the children sit together?

Question Number 134205 Answers: 0 Comments: 1

The numbers 1,2,3,4,5,6,7,8,9 and 10 are written around a circle in arbitrary order. We add all the numbers with their neighbours, we get 10 sums that way. What is the maximum possible value of the smallest of these sums?

$$ \\ $$The numbers 1,2,3,4,5,6,7,8,9 and 10 are written around a circle in arbitrary order. We add all the numbers with their neighbours, we get 10 sums that way. What is the maximum possible value of the smallest of these sums?

Question Number 133995 Answers: 0 Comments: 2

in how many ways can n men and n women be arranged in a row such that men and women alternate?

$${in}\:{how}\:{many}\:{ways}\:{can}\:{n}\:{men}\:{and} \\ $$$${n}\:{women}\:{be}\:{arranged}\:{in}\:{a}\:{row}\:{such} \\ $$$${that}\:{men}\:{and}\:{women}\:{alternate}? \\ $$

Question Number 133682 Answers: 0 Comments: 2

Question Number 133658 Answers: 0 Comments: 3

Question Number 133642 Answers: 4 Comments: 1

Question Number 133316 Answers: 2 Comments: 1

How many 6−letter words in which at least one letter appears more than once ,can be made from the letters in the word FLIGHT

$$\mathrm{How}\:\mathrm{many}\:\mathrm{6}−\mathrm{letter}\:\mathrm{words}\:\mathrm{in}\: \\ $$$$\mathrm{which}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{letter}\:\mathrm{appears} \\ $$$$\mathrm{more}\:\mathrm{than}\:\mathrm{once}\:,\mathrm{can}\:\mathrm{be}\:\mathrm{made}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{letters}\:\mathrm{in}\:\mathrm{the}\:\mathrm{word}\:\mathrm{FLIGHT} \\ $$$$ \\ $$

Question Number 133314 Answers: 1 Comments: 0

How many rearrangements are there of the letters in the world (i) ENGINEERING (ii) MATHEMATICAL

$$\mathrm{How}\:\mathrm{many}\:\mathrm{rearrangements}\:\mathrm{are}\: \\ $$$$\mathrm{there}\:\mathrm{of}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{in}\:\mathrm{the}\:\mathrm{world} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{ENGINEERING} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{MATHEMATICAL}\: \\ $$

Question Number 132977 Answers: 0 Comments: 0

Show that: ^n C_r =((Π_(k=0) ^(r−1) n−k)/(r!))

$$\mathrm{Show}\:\mathrm{that}: \\ $$$$\:^{{n}} {C}_{{r}} =\frac{\underset{{k}=\mathrm{0}} {\overset{{r}−\mathrm{1}} {\prod}}{n}−{k}}{{r}!} \\ $$

Question Number 132854 Answers: 1 Comments: 0

It is required to seat 5 men and 4 women in a row so that the women occupy the even place. How many such arrangements are possible ?

$$\mathrm{It}\:\mathrm{is}\:\mathrm{required}\:\mathrm{to}\:\mathrm{seat}\:\mathrm{5}\:\mathrm{men}\:\mathrm{and}\:\mathrm{4}\:\mathrm{women}\: \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{women}\:\mathrm{occupy}\:\mathrm{the}\:\mathrm{even}\: \\ $$$$\mathrm{place}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{such}\:\mathrm{arrangements}\:\mathrm{are} \\ $$$$\mathrm{possible}\:?\: \\ $$

Question Number 132726 Answers: 0 Comments: 0

use error fxn use polar coordinates to find ∫e^(−x^2 ) dx

$$\mathrm{use}\:\mathrm{error}\:\mathrm{fxn} \\ $$$$\mathrm{use}\:\mathrm{polar}\:\mathrm{coordinates}\:\mathrm{to}\:\mathrm{find} \\ $$$$\int\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx} \\ $$

Question Number 132439 Answers: 0 Comments: 1

it is a known that a particular machine will make product with a qualified rate of 90% when it is running well, but will do so with a qualified rate of only 30% when it is not running well. The probability that machine is running well is 75% normally . Suppose that one day the first product made by the machine is qualified. Find the probabiliy that the machine is running well at this time.

$$ \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{known}\:\mathrm{that}\:\mathrm{a}\:\mathrm{particular} \\ $$$$\mathrm{machine}\:\mathrm{will}\:\mathrm{make}\:\mathrm{product}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{90\%}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is} \\ $$$$\mathrm{running}\:\mathrm{well},\:\:\mathrm{but}\:\mathrm{will}\:\mathrm{do}\:\mathrm{so}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\:\mathrm{rate}\:\mathrm{of}\:\mathrm{only}\:\mathrm{30\%}\:\mathrm{when}\: \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{not}\:\mathrm{running}\:\mathrm{well}.\:\mathrm{The} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{machine}\:\mathrm{is}\: \\ $$$$\mathrm{running}\:\mathrm{well}\:\mathrm{is}\:\mathrm{75\%}\:\mathrm{normally}\:. \\ $$$$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{one}\:\mathrm{day}\:\:\mathrm{the}\:\mathrm{first}\: \\ $$$$\mathrm{product}\:\mathrm{made}\:\mathrm{by}\:\mathrm{the}\:\mathrm{machine}\:\mathrm{is}\: \\ $$$$\mathrm{qualified}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probabiliy}\: \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{machine}\:\mathrm{is}\:\mathrm{running}\:\mathrm{well}\:\mathrm{at} \\ $$$$\mathrm{this}\:\mathrm{time}.\: \\ $$

Question Number 132382 Answers: 1 Comments: 0

What is the coefficient x^(10) in the expansion of (1+x^2 −x^3 )^8

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{x}^{\mathrm{10}} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} −\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{8}} \\ $$

Question Number 132174 Answers: 0 Comments: 3

Question Number 131994 Answers: 2 Comments: 1

Question Number 131744 Answers: 1 Comments: 0

Question Number 131635 Answers: 0 Comments: 0

three subject group are to be formed randomly by 15 students (including 3 girls) under the condition that each groups consist 5 students and each student attends only one group. flnd the probabilities that of the following events (1) there is exactly one girl in each group (2) the 3 girls attend the same group

$$ \\ $$$$\mathrm{three}\:\mathrm{subject}\:\mathrm{group}\:\mathrm{are}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{formed}\:\mathrm{randomly}\:\mathrm{by}\:\mathrm{15}\:\mathrm{students} \\ $$$$\left(\mathrm{including}\:\mathrm{3}\:\mathrm{girls}\right)\:\mathrm{under}\:\mathrm{the} \\ $$$$\mathrm{condition}\:\mathrm{that}\:\mathrm{each}\:\mathrm{groups} \\ $$$$\mathrm{consist}\:\mathrm{5}\:\mathrm{students}\:\mathrm{and}\:\mathrm{each} \\ $$$$\mathrm{student}\:\mathrm{attends}\:\mathrm{only}\:\mathrm{one}\:\mathrm{group}. \\ $$$$\mathrm{flnd}\:\mathrm{the}\:\mathrm{probabilities}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{events}\:\left(\mathrm{1}\right)\:\mathrm{there}\:\mathrm{is} \\ $$$$\mathrm{exactly}\:\mathrm{one}\:\mathrm{girl}\:\mathrm{in}\:\mathrm{each}\:\mathrm{group}\:\left(\mathrm{2}\right) \\ $$$$\mathrm{the}\:\mathrm{3}\:\mathrm{girls}\:\mathrm{attend}\:\mathrm{the}\:\mathrm{same}\:\mathrm{group} \\ $$

Question Number 131553 Answers: 1 Comments: 0

Question Number 131464 Answers: 1 Comments: 0

determinant (((old plate : EEU 874)),((new plate : 1BXK 267))) Old California license plate consisted of a sequence of three letters followed by three digits (see figure above). Assuming that any sequence of letters and digits was allowed (though actually some combinations of letters were disallowed), how many license plate were available ?

$$\:\begin{array}{|c|c|}{{old}\:{plate}\::\:{EEU}\:\mathrm{874}}\\{{new}\:{plate}\::\:\mathrm{1}{BXK}\:\mathrm{267}}\\\hline\end{array} \\ $$$${Old}\:{California}\:{license}\:{plate}\: \\ $$$${consisted}\:{of}\:{a}\:{sequence}\:{of} \\ $$$${three}\:{letters}\:{followed}\:{by}\:{three} \\ $$$${digits}\:\left({see}\:{figure}\:{above}\right). \\ $$$${Assuming}\:{that}\:{any}\:{sequence} \\ $$$${of}\:{letters}\:{and}\:{digits}\:{was}\:{allowed} \\ $$$$\left({though}\:{actually}\:{some}\:{combinations}\right. \\ $$$$\left.{of}\:{letters}\:{were}\:{disallowed}\right),\:{how} \\ $$$${many}\:{license}\:{plate}\:{were}\: \\ $$$${available}\:? \\ $$

Question Number 131459 Answers: 1 Comments: 0

Eight eligible bachelor and seven beautiful models happen randomly to have purchased single seats in the same 15−seats row of theather. On the average , how many pairs of adjacent seats are ticketed for marriageable couples ?

$${Eight}\:{eligible}\:{bachelor}\:{and}\:{seven}\:{beautiful} \\ $$$${models}\:{happen}\:{randomly}\:{to}\:{have}\: \\ $$$${purchased}\:{single}\:{seats}\:{in}\:{the}\:{same}\:\mathrm{15}−{seats} \\ $$$${row}\:{of}\:{theather}.\:{On}\:{the}\:{average}\:,\:{how}\:{many} \\ $$$${pairs}\:{of}\:{adjacent}\:{seats}\:{are}\:{ticketed} \\ $$$${for}\:{marriageable}\:{couples}\:? \\ $$

Question Number 131248 Answers: 2 Comments: 0

If α and β are the coefficient of x^8 and x^(−24) respectively in the expansion of [ x^4 +2+(1/x^4 ) ]^(10) in powers of x then (α/β) is equal to

$${If}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{coefficient}\: \\ $$$${of}\:{x}^{\mathrm{8}} \:{and}\:{x}^{−\mathrm{24}} \:{respectively}\: \\ $$$${in}\:{the}\:{expansion}\:{of}\:\left[\:{x}^{\mathrm{4}} +\mathrm{2}+\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\:\right]^{\mathrm{10}} \\ $$$${in}\:{powers}\:{of}\:{x}\:{then}\:\frac{\alpha}{\beta}\:{is}\:{equal}\:{to}\: \\ $$

Question Number 131162 Answers: 0 Comments: 2

Five children sitting one behind the other in a five seater merry−go−round ,decide to switch seats so that each child has new companion in front. In how many ways can this be done?

$${Five}\:{children}\:{sitting}\:{one}\:{behind} \\ $$$${the}\:{other}\:{in}\:{a}\:{five}\:{seater}\:{merry}−{go}−{round} \\ $$$$,{decide}\:{to}\:{switch}\:{seats}\:{so}\:{that}\:{each} \\ $$$${child}\:{has}\:{new}\:{companion}\:{in}\:{front}. \\ $$$${In}\:{how}\:{many}\:{ways}\:{can}\:{this}\:{be}\:{done}? \\ $$

Question Number 130899 Answers: 0 Comments: 1

There are 20 persons at a party. Maria dansed with 7 boys, Stacy dansed with 8 boys, Monia dansed with 9 boys and Eve dansed with all the boys at the party. How many girls are there at the party ?

$$\mathrm{There}\:\mathrm{are}\:\mathrm{20}\:\mathrm{persons}\:\mathrm{at}\:\mathrm{a}\:\mathrm{party}. \\ $$$$\mathrm{Maria}\:\mathrm{dansed}\:\mathrm{with}\:\mathrm{7}\:\mathrm{boys}, \\ $$$$\mathrm{Stacy}\:\mathrm{dansed}\:\mathrm{with}\:\mathrm{8}\:\mathrm{boys}, \\ $$$$\mathrm{Monia}\:\mathrm{dansed}\:\mathrm{with}\:\mathrm{9}\:\mathrm{boys}\:\mathrm{and} \\ $$$$\mathrm{Eve}\:\mathrm{dansed}\:\mathrm{with}\:\mathrm{all}\:\mathrm{the}\:\mathrm{boys}\:\mathrm{at}\:\mathrm{the}\:\mathrm{party}. \\ $$$$\boldsymbol{\mathrm{How}}\:\boldsymbol{\mathrm{many}}\:\boldsymbol{\mathrm{girls}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{party}}\:? \\ $$

Question Number 130685 Answers: 2 Comments: 0

How many password containing 6 characters of the letters in the word ′′ Move Now ′′ ?

$${How}\:{many}\:{password}\:{containing} \\ $$$$\mathrm{6}\:{characters}\:{of}\:{the}\:{letters}\:{in}\:{the}\: \\ $$$${word}\:''\:{Move}\:{Now}\:''\:? \\ $$

Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12 Pg 13

Contact: info@tinkutara.com