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

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Question 870638: in how many ways the 3 books of math 2 books of chemistry and 2 books of physics can be placed in a shelf. so that the books of same subject are placed together
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Question 872326: In how many ways can 7 students be selected to individually answer questions on the board?
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Question 872403: A school committee of 5 is to be formed from 12 students.How many different committees can be formed if joe must be on the committee?
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Question 872371: in how many way can the offices of president, secretary and treasurer be filled from a group of nine people?
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Question 872435: In how many ways can 5 players be assigned to 5 positions on a baseball team, assuming any player can play any position?
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Question 872444: A restaurant offers a choice of 2 salads, 8 main courses, and three desserts. How many possible choices for a meal are there(including single items)?
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Question 872442: A school committee consists of five women and three men. In how many
ways can a subcommittee of four members be formed if:
a. Any four members can be chosen?

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Question 872451: I need help with this problem?
Five hundred runners line-up for the Boulder race. In how many ways can the top five finishers occur?

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Question 872522: There are twenty dogs in the “Top Dog Show”. Three of the dogs will be chosen as finalists for top honors. There are how many possible ways for a dog to be selected as a finalist?
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Question 872565: if a group of 10 students sit in a gym how many possible way can they be arranged
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Question 872548: Find the number of ways in which a committee of 4 can be selected from among 45 members of a college fraternity
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Question 872868: how many words can be formed from word successful where all s comes together
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Question 872934: How many ways can a committee of 2 boys and 3 girls be formed from a class of 18 boys and 12 girls?
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Question 873247: there are 14 people in an office with 6 different phone lines. if all the lines begin to ring at once how many groups of 6 people can answer these lines
please help, i don't even know where to begin to help my son

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Question 873512: How many integers from 3000 to 8999 inclusive contain no 7's?
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Question 873516: How many integers from 3000 to 8999 inclusive contain no 7's? ( Answer should be 3645)
Thank you!

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Question 873514: This is a two part question. I can only figure out a)
a) How many arrangements using all of the letters of the word "parallel" are possible
8!/(3!2!)=3360
b) How many of these arrangements have all of the "l's" together?
Thank you

Click here to see answer by richwmiller(17219) About Me 

Question 873636: Six friends are going to sit together in a roller coaster car that has six seats. In how many different arrangements can they sit?
6×6 or
6×5×4×3×2×1
How do I determine which to use?

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Question 873636: Six friends are going to sit together in a roller coaster car that has six seats. In how many different arrangements can they sit?
6×6 or
6×5×4×3×2×1
How do I determine which to use?

Click here to see answer by algebrakid(1) About Me 

Question 873645: I have three different crust and 3 different cheeses and 7 toppings. How many different combinations can I have if Ionly can have 1 crust and 1 topping. 3x3x7=63 but what about double, triple and multiple toppings. Do I do 3x3x7x6x5x4x3x2x1=45360 and this is how many different combinations there are?
Click here to see answer by ewatrrr(24785) About Me 

Question 873664: A theater company with 10 actors is putting on a play that has 4 roles. In how many different ways can the director assign actors to those roles?
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Question 873680: How many 8 symbol computer passwords can be formed using the letters A-J and the digits 2-6?
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Question 873806: There are 10 players on a softball team. How many ways can the first 4 batters be chosen?
Click here to see answer by harpazo(655) About Me 

Question 873927: How many two people debating teams can be chosen from six students?

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Question 873957: Find the number of ways of arranging the letters of the word CALENDAR in such a way that exactly two letters are present between L and D?
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Question 874077: how many different combinations of management can there be to fill the positions of president, vice president and treasurer of a tennis club knowing there are 16 eligible candidates
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Question 874151: what are the total amount of choices possible if an individual is to create a 4 digit password using the digits 0-9 inclusive but not using the digit 0 as the first character of the password
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Question 874373: How many different groups of students can show up for a seminar with an enrollment of 15
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Question 874477: How many different ways can you make a password using the letter ABC
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Question 874487: A track team has seven members. In how many ways could three team members line up for a relay race?
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Question 874484: Find the number of permutations possible for the letters M T A C and H
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Question 874504: In how many ways can you select two books to read from a shelf of ten books?
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Question 874506: How many permutations are there of the following word?
OBFUSCATION

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Question 874551: The kindergartdb teachers are decorating their bulletin boards with colorful pictures of baby animals and their names. If Ms. Smith is selecting 4 animals from a group of 12, how many different groups of 4 animals could she choose?
I have 12C4 as a combination and got 495. I dont know if this is correct, please help, thank you!

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Question 874478: How many 2-digit numbers can you make using the digits 1-6?
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Question 874555: in the lunch line, students can choose 1 out of 3 meats, 1 out of 4 vegetables, 1 out of 3 deserts, and 1 out of 5 drinks. how many lunch combinations are there?
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Question 874610: You have to pick 2 people to work with out of 15. How many different groups can you pick?
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Question 874610: You have to pick 2 people to work with out of 15. How many different groups can you pick?
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Question 874713: a dictionary is printed consisting of 7 letters words CRICKET. If the word are printed at the alphabetical order as in an ordinary dictionary, then the number of words before the word CRICKET IS ?
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Question 874669: How do I pair 16 people for breakfast over 15 weeks?
I can do it for 4,6 and 8 people. I can't find a pattern to move to 10 people. Here is 8:
Week 1 1,2 3,4 5,6 7,8
Week 2 1,7 2,4 3,6 5,8
Week 3 1,8 2,3 4,5 6,7
Week 4 1,4 2,6 3,8 5,7
Week 5 1,3 2,5 4,7 6,8
Week 6 1,6 2,7 4,8 5,3
Week 7 1,5 2,8 3,7 6,4

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Question 874753: you have a class of 20 students, a teacher wants to send 4 to get books for her, how many combinations of 4 students can she send?
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Question 874837: There were nine students running in a race.How many different arrangments of first,second,third,and fourth place are possible?
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Question 875079: For a string of n digits in a binary system (1s and 0s), what is the equation determining the number of permutations of the string for every n?
For example, in a 3-digit string, there are 8 permutations possible:
000
001
010
011
100
101
110
111
How can I determine the number of permutations for longer strings? I'm hoping to have an equation good for all n.

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Question 875068: Katie likes to wear odd socks. She can choose two non-matching socks from a drawer with six different, separated pairs of socks in how many ways?
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Question 875158: in how many ways can 6 people (A,B,C,D,E and F)be seated at a round table ? suppose that two arrangements are different if at least one person has diffeent neighbors.
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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