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

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Question 266394: How many ways can 6 students desks be arranged in a row? explain
Click here to see answer by checkley77(12844)

Question 266416: find the number of permutations of letters of CALENDAR in which C and A are together but N and D are not?
Click here to see answer by Edwin McCravy(20054)

Question 266699: My computer password has a letter followed by 5 digits and then another letter. If there are no repeats, then how many possible such computer passwords are there?
Click here to see answer by Edwin McCravy(20054)

Question 266712: The town that I live in has the type of facility that produces license plates. Assume that all license plates are required to have the following format: LLNNNL, where �L� stands for a capital letter and �N� stands for a single digit number (0 through 9). How many unique license plates can be produced by the facility in my town?
Click here to see answer by Alan3354(69443)

Question 267348: how many combinations can u arrange 7 books on a shelf

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Question 267348: how many combinations can u arrange 7 books on a shelf

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Question 268160: In how many ways can a student answer 8 true or false questions on a test?
Click here to see answer by drk(1908)

Question 268980: How many improper subsets (including the set itself) are possible for the set (a,b,c,d)?
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Question 268998: There are six multiple-choice questions on an exam, each with three possible answers. Determine the number of possible answer sequences for the six questions
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Question 269023: If you have 5 bowlers on a team, how many ways can the lineup be ordered? Keep in mind that the strongest of the five should always be the last in the lineup.
Click here to see answer by checkley77(12844)

Question 269228: You wish to split the numbers [1,2,3,4,5,6,7,8] into two sets of 4 numbers, such that the following 2 conditions are satisfied.
� The sums of the numbers in both sets are equal
� The sums of the squares of the numbers in both sets are equal
I have found the two sets of nymbers [1,4,6,7] and [2,3,5,8] but i cannot find a relationship between the sets that will enable me to split the original list.
Help please !!
Click here to see answer by dabanfield(803)

Question 269300: There are 15 players on a baseball team. How many ways are there to select 9 players for the starting lineup? (answer in back says 362,880, but I cannot get that answer!)
Click here to see answer by stanbon(75887)

Question 270201: Find n, C(n,6):C(n-3,3)=91:4
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Question 270349: In how many ways can a group of 5 boys and 5 girls be seated in a row of 10 seats if boys and girls must alternate in the row?
Click here to see answer by josmiceli(19441)

Question 270350: An urn contains 4 red, 2 white, and 2 blue marbles. In how many ways can three marbles be selected so that at least one of them is blue?
Click here to see answer by Edwin McCravy(20054)

Question 271307: If you have a 30 digit number and 0-9 are represented equally so there are three of each number how would you calculate how many permutations there are with no repeats so for example: aaabbc if this was a permutation and you were listing all the permutations you wouldn't want to list representations of all three a's at the beginning. so instead of listing aaabbc aaabbc aaabbc you would only list it once. How would you calculate this for the example given at the beginning and how would you calculate it so that 0 wouldn't have been in the first position. So like if you had a 5 digit number 01234 wouldn't happen. I know how to do permutations, so for a 30 digit number it would be 30!, but with these added rules I am having a hard time. Thank you for your time.
Click here to see answer by stanbon(75887)

Question 271489: How many ways can a president and vice-president be selected in a class of twenty students?
Click here to see answer by Edwin McCravy(20054)

Question 271956: Use binomial expansion to expand the following (2x-3y)^4
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Question 271956: Use binomial expansion to expand the following (2x-3y)^4
Click here to see answer by Edwin McCravy(20054)

Question 272080: How many 4-number license plates can be made using the digits 0, 1, 2, 3, 4, and 5, if an even digit must come first and repetitions are allowed? Not allowed?
Click here to see answer by checkley77(12844)

Question 272057: The probability of rain in a certain city is 1/8 on a given day. Find the probability that rain will fall on exactly one day of a three day visit.
Click here to see answer by rfer(16322)

Question 272230: 3 single men, 2 single women and 2 families each consisting of 2 parents and 1 child are to be seated at a round table. how many different seating arrangements are there if the families were to sit together and the women must be seperated?
Click here to see answer by coolcat1998(1)

Question 272415: How many 3-letter code words are possible using the first 8 letters of the alphabet if letters can be repeated?
Click here to see answer by scott8148(6628)

Question 272477: in how many ways can 10 people be chosen for a 3 person committee
Click here to see answer by dabanfield(803)

Question 272662: A computer password consist of six characters.The first two must be lower case letters and the remaining four can be either digits or lower case letters. how many different passwords are possible?

Click here to see answer by Theo(13342)

Question 272881: There are 15 irish dancers in a championship-level competition. How many ways can the top 3 finishers be arranged?
Click here to see answer by edjones(8007)

Question 273140: in many lotteries, contestants choose 6 out of 50 numbers, without replacement.
find the probability of winning this kind of lottery with one set of numbers.
Click here to see answer by solver91311(24713)

Question 273156: In the United Kingdom's National Lottery you must correctly select a group of 6 numbers from 49. Suppose that the contest were changed to selecting 7 numbers. How many more ways would there be to select the numbers?
Click here to see answer by solver91311(24713)

Question 273360: if ten digits 0 to 9 are arranged randomly with no repetition of digits how many different arrangements are possible?
Click here to see answer by Edwin McCravy(20054)

Question 273384: 6 characters in a license plate, three letters followed by three numbers, how many possile registered cars.
Click here to see answer by checkley77(12844)

Question 273656: How many ways can a 6-person kickball team be chosen from 27 students?Is this a combination or permutation?
Click here to see answer by stanbon(75887)

Question 273957: How many 5-cards hands having exactly 3 aces and 2 other cards can be dealt?
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Question 274302: Aji has an argument with his daughter. She says, "you do the same thing every day." Aji does fishing every day but contends that every day is different because he does things in a different order each day.
Before he leaves shore in his row boat,
3 things
he gets fresh bait, checks the weather, and adjusts his seat cushion.
Out in the water,
4 things
he eats his fruit, puts meat on his sandwich, drinks his apple juice, and eats his sandwich.
Back at shore,
3 things
after tying his boat to the dock, he puts up the fishing pole in his right hand and the ice chest in his left hand.
Then he finally heads back home to have the same argument with his daughter. For how many days could Aji do things in a different order before he has to repeat the order of some prior day?
Click here to see answer by richwmiller(17219)

Question 274620: On a math test there are 5 multiple-choice questions with 10 possible answers and 15 true�false questions. In how many possible ways can the 20 questions be answered?
Click here to see answer by josmiceli(19441)

Question 274645: Seating in a Movie Theater
How many different ways can 5 people--A,B,C,D and E-- sit in a row at a movie theater if (a) A and B must sit together; (b) C must sit to the right of, but not necessarily next to B; (c) D and E will not sit next to to each other?

Thank you,
Click here to see answer by Edwin McCravy(20054)

Question 274742: how many ways can you choose 3 different letters from the alphabet to arrange on a car tag?

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Question 274970: There are 5 places in a event. Each place can be won by a man or women. What are the outcomes?
Click here to see answer by dabanfield(803)

Question 276324: Consider a political discussion group consisting of 6 Democrats, 4 Republicans, and 3 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting an Independent and then a Democrat.
Click here to see answer by edjones(8007)

Question 276952: Fifteen dogs enter a Goofy Dog contest. In how many different ways can a champion, a first runner-up, and a second runner-up be selected?
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Question 276981: A survey of 51 pet owners revealed that 32 owned dogs, 38 owned cats, and 3 owned neither dogs nor cats. How many owned both dogs and cats?
Click here to see answer by edjones(8007)

Question 276980: In how many ways can 10 letters: 2 C�s, 3 D�s, and 5 F�s be awarded to 10 politicians, one letter for each politician?
Click here to see answer by edjones(8007)

Question 276988: In how many different ways can a panel of 12 jurors and 2 alternates be chosen from a group of 20 prospective jurors?
Click here to see answer by edjones(8007)

Question 276989: A student planning her curriculum for the upcoming year must select one of five business courses, one of three mathematics courses, two of six elective courses, and either one of five history courses or one of three social science courses. How many different curricula are available for her consideration?
Click here to see answer by solver91311(24713)

Question 277145: how many six digit numbers...
a. contain 7 at least once
b. start and end with a 7
c. have alternating 7 and non 7 digits
Click here to see answer by Edwin McCravy(20054)

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