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

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Question 717606: Find the number of of arrangements of the letters of the word NATIONAL if the N's must come together
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Question 717585: If you have one $50 bill, one $20 bill, one $10 bill and one $100 bill, how many possible sums of money consisting of three bills each, can be formed?
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Question 717581: From 5 statisticians and 6 economists, a committee consisting of 3 statisticians and 2 economists is to be formed. How many different committees can be formed if:
a. two particular statisticians must be in the committee?
b. one particular economist cannot be in the committee?

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Question 717583: In how many ways can a group of 10 people be divided into:
a. two groups consisting of 7 and 3 people?
b. three groups consisting of 4, 3, and 2 people?

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Question 717769: Please how do i recognise if a question is permutative or Combinative
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Question 717781: Q4. No. of words that can be formed using all the letters of the word GARGEE
if no two alike letters are together.
Ans is 84.

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Question 717822: There are 9 players on a volleyball team. Only 6 players can play at one time. The players are going to pick the team randomly. How many combinations of 6 player teams can be chosen?

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Question 718031: Find the indicated values.
(a) 9P2

(b) 9C2

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Question 718103: Q} Number of ways in which 8 students can be divided into 2 teams , that need not necessarily be of equal size.
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Question 718145: If you can buy 2 of the pets out of 4 breeds . How many possible outcomes could you have ?
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Question 718179: Number of ways in which 8 students can be divided into 2 teams , that need not necessarily be of equal size.
Ans 127
My method
As 8 student is divided into 2 teams
Team A==============Team B
1 =============== 7 students===== 8C1*7C7 - equation(1)
2 =============== 6 students ===== 8C2 -(2)
3 =============== 5 students ===== 8C3 -(3)
4 =============== 4 students ===== 8C4 -(4)
5 =============== 3 students ===== 8C5 -(5)
6 =============== 2 students ===== 8C6 -(6)
7 =============== 1 student ===== 8C7 -(7)
Therefore no. of ways = (1)+(2)+(3)+(4)+(5)+(6)+(7)=252
But actual answer is the half of this answer.Can you tell me where I go wrong?

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Question 718477: How many ways can you answer a 10 question multiple choice test?
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Question 718643: 8 people from a group of 12
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Question 718747: There are 36 dogs entered in a show where there will be a first, second, and third place award. How many possiblites are there or these awards?
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Question 719310: Find the number of permutations of all the letters in the word TREASURE.
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Question 719749: 10!
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Question 720627: In How Many Ways 50 things Can Be divided In 5 sets,such That 3 sets Contain 12 things each and the remaining 2 sets contain 7 things each?
Click here to see answer by Edwin McCravy(20054) About Me 

Question 720901: Explain how you would find out how many committees of 4 boys and 2 girls can be found from a group of 5 boys and 8 girls.
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Question 721071: Student Painters, which specializes in painting the exterior of residential buildings, has eight people available to be organized into six-person and two-person teams. In how many ways can the company organize the available people into six- or two-person teams?
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Question 721731: A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 10 stocks?
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Question 721731: A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 10 stocks?
Click here to see answer by solver91311(24713) About Me 

Question 721792: If p, r and s are three different prime numbers greater than 2, and n= p*r*s, how many positive factors, including one and n, does n have?
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Question 721844: a roller coaster has room for 10 people. the people sit single file, one after the other. how many different arrangements are possible for 10 passangers on the roller coaster
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Question 721891: in how many ways can people chosen from a group of 8 be voted President, Vice President, and Secretary?
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Question 721888: In how many ways can a committee of 5 be made from a group of 12?
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Question 722523: seven boys and seven girls went to watch a movie. How may ways can they be seated if grace and joey are members of the group and want to sit together all the time?

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Question 722536: how many different three digit combinations can be made by using the numbers 1,3,5,7, and 9 without repetitions. Thank you!
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Question 723278: How many combinations of two books can be chosen from a group of four on a shelf?
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Question 723673: seven performers A,B,C,D,E,F and G are to appear in a talent contest. the order of appearance is by random selection. find the probability of the following events:
a. C will perform first
b. F or G will perform first
c. they will appear in the order C,D,E,A,B,F,G

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Question 725224: What's the probability that a poker hand(5 card draw) contains nothing but aces and eights?
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Question 725529: How do I solve 10! (Factorial)
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Question 725623: A student planning her curriculum for the upcoming year must select one of seven business courses, one of three mathematics courses, two of eight elective courses, and either one of two history courses or one of three social science courses. How many different curricula are available for her consideration?
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Question 725718: I'm trying to solve this question: A pizzeria offers 15 diffrent toppings. How many ways can a customer order 3 diffrent toppings. I attempted to use the counting principle 15!divided by (15-3)! but it didn't really make sense. Can you please explain it to me? I want to make sure I'm using the right formula.
Click here to see answer by Edwin McCravy(20054) About Me 

Question 725743: I have a question. So I have a problem that requires me to find the possibilities for opening a combination lock with numbers 0-39. it has to have three numbers. I tried 40*40*40 is that right?
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Question 725946: Evaluate the expression.
140P1

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Question 725948:
In how many ways can a chairperson and a vice chairperson be selected from a committee of 30 senators?

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Question 726054: If 3 melons sell for $0.42, how much would 7 melons cost?
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Question 726056: A club with 34 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many ways can this be done?
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Question 726819: political polling organization wishes to select a smaller focus group from a group of of 7 Republicans, 3 Democrats, and 4 Independents. In how many ways can the group be chosen if:
a) it will consist of 4 Republicans and 3 Democrats?
b) it will consist of 2 Republicans, 2 Democrats, and 3 Independents?

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Question 726817: How many three-letter "words" can be made from the 9 letters FGHIJKLMN if repetition of letters:
(a) Is allowed?
Your answer is :729
(b) Is not allowed?
Your answer is : 504

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Question 726821: A box contains 21 yellow, 28 green and 38 red jelly beans. If 14 jelly beans are selected at random, find each of the following probabilities.
a) The probability that 2 are yellow is: .
b) The probability that 2 are yellow and 11 are green is:
c) The probability that at least one is yellow is:

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Question 726779: serial numbers assigned to calculators by a manufactur have as a first symbo one of the letters J, H, T to indicate the plant in which made, followed by one of the numbers 01, 02....12, to indicae the plant in which made, followed by four digits. how many different serial numbers are possible ?
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Question 726733: Evaluate the expression
19c18

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Question 500253: You have the word FEEBLENESS, in a random arrangement, what is the probabilty that exactly three E's will be together?
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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