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

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Question 512737: The calibration of a filling machine broke, causing it to underfill 5 jars of jam. The jars were accidentally mixed in with 13 properly filled jars. All the jars look the same. 3 jars are chosen from the batch and weighed. What is the probability that exactly 2 jars are underweight?
Round your answer to 3 decimal places.

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Question 512856: Find the number of words that can be formed by considering all possible permutations of the letters of the word 'FATHER'. How many of these words begin with A and end with R?
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Question 513228: how many arrangements are there of the letters in DATAMANAGEMENT?
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Question 513334: Four students from Mrs.Wilson's class will be chosen to lead the opening song at an assembly. The students beng considered are John, Lee. Eric. Kyle, Nikki and Shelby. How many different 4 person groups can be formed from 6 students?
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Question 513801: How many ways can the letters A, B, C, D, E, and F be arranged in a row 4 at a time if neither A, nor C can be first or third and D cannot be fourth? Repetition is permitted.
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Question 513832: Robil can do 2 jobs in 3 days, and Buray can do 5 jobs in 6 days. Robil works for 3 days and then Buray begins to help. How many days will it take to complete a total of 74 jobs?
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Question 513832: Robil can do 2 jobs in 3 days, and Buray can do 5 jobs in 6 days. Robil works for 3 days and then Buray begins to help. How many days will it take to complete a total of 74 jobs?
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Question 514234: If a license plate is made up of three letters followed by 3 digits , how many license plate can be made if letters and numbers can be reapeted
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Question 514426: 15 persons in a club sit every day in dinner table such that every
member has different neighbor. This arrangement will last for how many
days.

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Question 514616: How many positive integers less than 150 are there such that all of the digits are odd?
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Question 514613: How many ways can the digits 1, 2, 3, 4, and 5 be arranged in a row of 3 to form an odd counting number if repetition is permitted and if 3 cannot be second and 1 cannot be third?
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Question 514818: a license plate has seven possible places how many license plates can be made if only two numbers are used example 1222121 and every slot must be filled to equal a seven digit number
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Question 514874: In how many ways can 6 men and 4 women sit in a row if the men must sit together and the women must sit together.
I thought it was 6!4! = 17280 possible arrangements but now I am second guessing.
Thanks for your help!

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Question 515147: How many ways can the letters A, B, C and D be arranged in a row if B cannot be in second place and repetition is not allowed?
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Question 515151: How many positive integers are there less than 800 such that all the digits are odd?
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Question 515224: their are six people getting on a bus, there are 8 seats, how many different possibilities are there

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Question 515659: so how many movies on 15 alphabet
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Question 516887: How many permutations can be formed from the letters of the word committee?
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Question 517750: How many ways can 4 baseball players and 3 basketball players be selected from 12 baseball players and 9 basketball players?
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Question 517835: There are 36 different choices each can be chosen more than once how many different combination can you make when you can only choose 10?
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Question 517839: if group 1 consists of 51 objects, group 2 consists of 47 objects, and group 3 consists of two objects. How many committees can be formed if each committee must have 5 of group 1 and 4 of group 2?
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Question 518160: A computer lab has 10 computers. How many ways can the computers be assigned to a group of 15 students?
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Question 518319: 1)There are 3 letters which have to be put into 4 boxes. In how many ways can be this done?Pls explain
2)there are 5 posts to be assigned to 6 candidates.In how many ways can be this done?Pls explain

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Question 518277: Find the number of ways of forming a group of 10 people from 15 couples if each group contains
i) no couples
ii) exactly 2 couples
THANKS!!!

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Question 518485: How many five-letter permutations can be formed from the first ten letters of the alphabet?
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Question 519221: How many ways can 7 students be assigned a seat in a classroom if there are 10 seats in a row?
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Question 519016: (a) In a certain province,license plates consist of three letters (A-Z) and three digits (0-9). How many different plates can be issued? (b) If the province allows any six character mix (in any order) of 26 letters and 10 digits, how many unique plates are possible?
Thanks for the help

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Question 519767: Question: How many ways can 3 students be placed in a row of 5 desk?
I tried the standard way, like if you had 5 students in 5 desk, you do 5x4x3x2x1, but I didn't get how to do this problem.

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Question 520478: Can you please help me to understand if I am doing this correctly?
1.In how many ways can 4 girls and 3 boys be seated ina row if boys cannot sit together and girls cannot sit together? 4*3=12?
2.In how many ways can 4 girls and 3 boys be seated in a row if girls must sit in the end seats? 4!*3!=144?
3.In how many ways can 4 girls and 3 boys be seated in a row if girls muct sit with girls and boys must sit with boys? 4*3=12?
4.A driver is going from Natchitoches, LA to El Dorado, Arkansas by way of Shreveport. How many different routes can the driver make on their trip if they have 3 different routes from Natichtoches to Shreveport and five different routes from Shreveport to Eldorado?
Thanks,
Rebecca

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Question 520478: Can you please help me to understand if I am doing this correctly?
1.In how many ways can 4 girls and 3 boys be seated ina row if boys cannot sit together and girls cannot sit together? 4*3=12?
2.In how many ways can 4 girls and 3 boys be seated in a row if girls must sit in the end seats? 4!*3!=144?
3.In how many ways can 4 girls and 3 boys be seated in a row if girls muct sit with girls and boys must sit with boys? 4*3=12?
4.A driver is going from Natchitoches, LA to El Dorado, Arkansas by way of Shreveport. How many different routes can the driver make on their trip if they have 3 different routes from Natichtoches to Shreveport and five different routes from Shreveport to Eldorado?
Thanks,
Rebecca

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Question 520572: How many bit strings of length 9 either begin with 2 bit(s) equal to 0 or end with 3 bit(s) equal to 1?
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Question 521111: I Got 2 Questions.
1.In a gym class, there are 12 boys and 18 girls. If the teacher selects 1 student from her class at random, what is that the student will be a boy?
2.In a bag of candies there are 7 candies, 4 green candies, 2 yellow candies, and 3 blue candies. If you choose 1 candy from the bag, put it back, draw another candy. What is the probability that they will BOTH be yellow?

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Question 521409: a standard deck of 52 cards is selected and one card is drawn.what is the probability that the card is an ace or a face card?
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Question 521478: If there are three roads from Goshen to Gravette and two roads from Gravette to Tontitown, how many ways are there to go from Goshen to Tontitown through Gravette?
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Question 521787: You order twelve burritos to go from a Mexican restaurant, five with hot peppers and seven without. However, the restaurant forgot to label them. If you pick three burritos at random,
a. find the probability that at least one has hot peppers.
b.find the probability that exactly two have hot peppers.
c. find the probability that none has hot peppers.

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Question 521789: wo hundred people apply for three jobs. Sixty of the applicants are women. If three persons are selected at random,
a.what is the probability that all are women?
60C3 / 200C3
(60C3 * 140C1) / 200C3
(60C1 * 140C3) / 200C3
60C3 / 140C1
None of the above



b.what is the probability that two are women?
60C2 / 200C3
(60C1 * 140C2) / 200C3
(60C2 * 140C1) / 200C3
(60C2 * 200C1) / 200C3
None of the above
Find the expected value of each $1 bet in roulette: the five – number bet.
-$0.0526316
-$0.0789474
-$0.243157
-$0.710526
-$1.65789
please explain how you get the answers

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Question 522114: In how many ways can 3 of 10 people be elected to the positions of president, secretary, and treasurer?
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Question 522114: In how many ways can 3 of 10 people be elected to the positions of president, secretary, and treasurer?
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Question 522278: A true/false test has 15 questions. Assuming that we do not care about the score of the test, in how many different ways can the test be completed?
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Question 522406: A professor writes 40 discrete mathematics true/false
questions. Of the statements in these questions, 17 are
true. I f the questions can be positioned in any order, how
many different answer keys are possible?

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Question 522406: A professor writes 40 discrete mathematics true/false
questions. Of the statements in these questions, 17 are
true. I f the questions can be positioned in any order, how
many different answer keys are possible?

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Question 522691: Ron's computer password must contain three lowercase letters followed by four numerical digits. If repetition is permitted how many differand passwords are possible?
If repetition is not permitted how many different passwords are possible?

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Question 522146: Algebra Foundamentals Counting
how many different ways can the letters of the word COUNTED be arranged?

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Question 523120: I've tried this numerous of time but I just can't figure it out. A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the specified type. Straight (five cards of consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A, not all of the same suit) (Note that the ace counts either as a 1 or as the denomination above king.)
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Question 523226: A classroom building has 7 different doors. In how many ways can a student enter by one door and exit by a different door?
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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