Questions on Algebra: Combinatorics and Permutations answered by real tutors!

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Question 1147173: There are two round tables, one oak and one mahogany, each with five seats. In how many ways may a group of ten people be seated?
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Question 1147274: Four adults are standing in a room that has five exits. Each adult is equally likely to leave the room through any one of the five exits.
b)What is the probability that three particular adults use the same exit and the fourth adult uses a different exit?
c) What is the probability that any three of the four adults come out the same exit, and the remaining adult comes out a different exit?
d) What is the probability that no more than two adults come out any one exit?
Thank you in advance!!!

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Question 1147296: Write the following expression without using the factorial symbol
(n-4)!/3!(n-2)!

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Question 1147294: Solve for n
n!/4!(n-2)! =3

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Question 1147294: Solve for n
n!/4!(n-2)! =3

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Question 1147294: Solve for n
n!/4!(n-2)! =3

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Question 1147298: How many ways can 5 teddy bears, 6 toy trucks, 5 dolls, and 1 toy car be distributed among 17 children if each child is to receive one item?
must show work

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Question 1147297: Write the following expression without using the factorial symbol
nC3+nC2+nC1

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Question 1147295: Solve for n
nP4=84 nC2 *show work using factorial notation

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Question 1147272: A senate committee of five members is to be selected from N Labor and five Liberal senators. Use trial and error to find the minimum value of N, given that the probability of Labor having a majority on the committee is greater than 3/4 .
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Question 1147324: Write the following expression without using factorial notation. Please show all work.
(n-4)!/3!(n-2)!

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Question 1147553: How many ordered lists are there of five items chosen from nine?
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Question 1147553: How many ordered lists are there of five items chosen from nine?
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Question 1147556: Find how many arrangements of the letters of the word FOUNDER are possible if the R is somewhere to the right of the U.
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Question 1147711: Please help me solve: A committee consisting of 3 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 11 faculty members and 13 students eligible to serve on the committee. In how many ways can the committee be formed?
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Question 1147706: A catering service offers 3 appetizers, 5 main courses, and 10 desserts. A customer is to select 2 appetizers, 4 main courses, and 5 desserts for a banquet. In how many ways can this be done?
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Question 1147834: given nPr=3024 and nCr=126 find n and r
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Question 1147834: given nPr=3024 and nCr=126 find n and r
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Question 1147877: five of the eight students in middle georgia state college. what is the probablity that all four of the interviewed students are from middle georgia state college
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Question 1148146: How many unordered sets are there of two items chosen from four?

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Question 1148275: A student planning her curriculum for the upcoming year must select one of six business courses, one of two mathematics courses, two of seven elective courses, and either one of three history courses or one of two social science courses. How many different curricula are available for her consideration?

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Question 1148275: A student planning her curriculum for the upcoming year must select one of six business courses, one of two mathematics courses, two of seven elective courses, and either one of three history courses or one of two social science courses. How many different curricula are available for her consideration?

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Question 1148285: A company car that has a seating capacity of seven is to be used by seven employees who have formed a car pool. If only three of these employees can drive, how many possible seating arrangements are there for the group?
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Question 1148437: A group of 7 people are to be put into a line. Among these people are Doc, Frank and Shem. What is the probability that the 1st 3 people in order are Doc, Frank and Shem?
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Question 1148437: A group of 7 people are to be put into a line. Among these people are Doc, Frank and Shem. What is the probability that the 1st 3 people in order are Doc, Frank and Shem?
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Question 1148573: What is the term containing x6 in the expansion of (x+2y)10.
Thanks

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Question 1148564: Imagine that you need to create a pin code that consists of 6 numbers. How many different pin codes can you createif
1. There are no restrictions?
2. None of the numbers can repeat?
3. None of the digits can be even?
4. The first digit cannot be a 3 or 2 and the last digit cannot be a 9?
5. The first digit cannot be a 2 and none of the digits can repeat

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Question 1148640: how many different id cards can be made if there are four digits on a card and no digit can be used more than once
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Question 1148640: how many different id cards can be made if there are four digits on a card and no digit can be used more than once
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Question 1148666: There are 4 different mathematics books and 5 different science books in how many ways can the books be arranged on a shelf if?

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Question 1148680: how many distinguishable permutations of letters are possible in the word ENGINEERING?

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Question 1148761: Six different books will be displayed in the library window. How many different arrangements are there?

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Question 1149084: There are 8 true-fales questions in an examination.how many responses are possible?

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Question 1149277: Seven orchids from a collection of 23 are to be selected for a flower show. Complete parts​ (a) and​ (b) below
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Question 1149279: Seven orchids from a collection of 23 are to be selected for a flower show. Complete parts​ (a) and​ (b) below
a) In how many ways can this be​ done?
b.) How many ways can the 7 be selected if 3 special plants from the 23 must be​ included?

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Question 1149391: If you are allowed to use numbers 1 - 9 and need to choose the passcode of an exact 4 digit code, how many possibilities are there?
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Question 1149503: A committee of 5 people is selected from a group of 7 men and 8 women. In how many ways can the committee be selected so it contains at least 1 woman?

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Question 1149518: Find how many groups of one or more digits can be formed from the following digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if repetition is not allowed
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Question 1149518: Find how many groups of one or more digits can be formed from the following digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if repetition is not allowed
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Question 1149516: Tom and Jerry and five other people get on a bus one at a time. How many ways can the seven get on the bus if Tom gets on the bus after Jerry
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Question 1149515: Out of thirty consecutive integers, how many ways can three numbers be selected whose sum is odd?
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Question 1149527: An urn contains 12 distinguishable cubes of which 5 are red and the remainder is black. If a random sample of 6 cubes is drawn without replacement, calculate the probabilities of 3 redcubes in the sample
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Question 1149533: Seven-letter words can be formed without repetition from the letters of the word INCLUDE; 5040. How many have the letters N and D separated by exactly two letters?
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Question 1149533: Seven-letter words can be formed without repetition from the letters of the word INCLUDE; 5040. How many have the letters N and D separated by exactly two letters?
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Question 1149532: Of the seven-letter words that can be formed without repetition from the letters of the word INCLUDE
how many have the letters N and D separated by more than two letters?

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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035