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

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Question 348557: A sample of 5 balls is to be selected at random from an urn containing 20 balls numbered 1 to 20. Four balls are green, 6 balls are white, and 10 balls are black.
How many samples can be selected that contain at least 1 white ball?
I wrote out all the sample spaces and tried to count them, but that didn't work for me, i must have missed some.

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Question 349585: how many ways does 5 persons can seat in round table?
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Question 349931: A Social Security number is used to identify each resident of the United States uniquely. The number is in the form xxx-xx-xxxx, where each x is a digit from 0 to 9. How many Social Security numbers can be formed?
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Question 349970: I need help with three probability questions.
First question says how many license plate become available if repetition is allowed?
second question says how many license plate become available if reppetition is not allowed?
last question says how many license plate become available if repetition is allowed but adjacent letter or number has to be different?

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Question 350157: I have 5 types of flowers and three flowers will be in each vase. How many vases will there be?

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Question 350208: A salad bar has 15 ingredient s . How many unique salads can be made?
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Question 350659: How many ways can 8 elementary school students (4 boys and 4 girls) and their teacher be lined up against a wall to have their picture taken if the teacher must be on one of the ends?
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Question 350656: A teacher has 7 students. They pose for a picture by standing in a single line. If the teacher stands on either end of the line, how many different arrangements of the 8 people are possible?
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Question 350844: b) How many ways are there to distribute 20 district object into 10 distinct boxes with
i) At least two empty box.
ii) No empty box.

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Question 350843: Find how many 3 digit numbers are even? Also find how many 4 digit numbers are composed of odd digits?
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Question 350590: if the letters of the word 'MOTHER'are written in all possible order and these words are written out as in dictionary ,find the rank of the word 'MOTHER'.
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Question 349633: 5 women and 6 men are on a softball team. Two of them are brothers. How many ways can you form a committee of 2 women and 3 men if you keep the brothers together, either both on the committee or both off the committee? What is the probability that the committee will have 2 women and 3 men and that the brothers will be together, either both on the committee or both off the committee?
I tried 5C3 x 5C2 for the first part and (5C3 x 5C2)11C5 for the second part but I don't think it's right. Any help would be greatly appreciated.
Thanks

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Question 349036: An employer has 8 different tasks that he wants completed by his four employees. Each of the tasks is to be done by one employee. The employer wants to distribute the tasks so that each employee gets assigned at least one task but not more than three tasks. How many different ways are there to assign the 8 tasks?
I attempted to draw a tree diagram to get the solution to this problem but I believe that led me in the wrong direction. How do i solve this using the correct formula?

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Question 349185: Find the rank of MOTHER ? and also find the rank of BHARAT?
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Question 348555: An employer has 8 different tasks that he wants completed by his four employees. Each of the tasks is to be done by one employee. The employer wants to distribute the tasks so that each employee gets assigned at least one task but not more than three tasks. How many different ways are there to assign the 8 tasks?
I attempted to do a tree diagram but that got messy and confusing and didnt get me the answer

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Question 348168: (color) red white blue
(size) small medium large extra large
the table above shows the different colors and sizes of t-shirts that are available at independence high school. how many different combination's of color and size are possible?
a 7 b 12 c 15 d 25 e 64

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Question 348123: How many ways can you arrange 6 men and 9 women seated on a round table and 2 mens are not seated to each other? thank you very much
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Question 347939:
In how many ways can 7 different contracts be distributed among 12 different firms, if any one firm can be awarded multiple contracts?

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Question 347936:
An urn contains 3 red, 1 white, and 4 blue marbles. In how many ways can 2 red and 3 blue marble(s) be selected?

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Question 347860: How many arrangements of the letters in the word COUNTING are possible?
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Question 342639: In how many ways can a committee of 5 people be chosen from 7 men and 3 women if it must contain at least one woman?
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Question 342414: In how many ways can 12 poeple be divided into 3 groups of 4 persons(in each group)?
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Question 341008: How many four-digit odd integers greater than 6000 can be formed from the digits 0,1,3,5,6 and 8, if no digit can be used more than once?
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Question 351069: a club member has 12 members. in how many ways can a president, vice president, and a secretary be chosen?... is it 12X11X10
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Question 349982: Joey and Ross along with 4 other best friends go to see a movie. They find a row of 6 seats, but Joey and Ross don’t want to sit next each other. How many different seating arrangements are possible if Joey and Ross don’t want to sit next each other?
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Question 351011: If 2n teams are to be assigned to play in 1, 2, 3, .... n games in the first round of a bracket, how many ways can the teams be assigned to the games?
thanks

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Question 347938:
In how many ways can a group of 4 boys and 4 girls be seated in a row of 8 seats?

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Question 347940:
In how many ways can 5 different contracts be distributed among 9 different firms, if no two contracts are awarded to the same firm?

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Question 348171: How many different ways can you seat 9 people in 4 chairs? I do not understand what equasion to use.
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Question 346759: In how many ways can someone pick 5 cubes out of 5 red and 5 orange cubes, if at least one cube of each color has to be picked? Thank you.
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Question 351383: how many words can be made by rearranging he letters in the word "minimum"?
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Question 351387: how many 9 letter words can be formed by permuting the letters of "territory"?
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Question 351393: in how many ways can a group of 6 people arrange themselves in a circle, holding hands for a group dance?
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Question 351884: how many possible combinations are there if you choose one sandwich one fruit and one drink with 2 choices of each
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Question 351470: A student is required to work exactly 7 problems from a 14-problem exam and must work exactly 3 of the first 4 problems. In how many ways can the seven problems be chosen?
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Question 351397: how many seating arrangements are possible for 5 children and their mother in a 9 seat van if the mother must be the driver?
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Question 352191: In how many ways can a committee of 7 be formed if there are 10 dogs and 15 cats to choose from and the committee must consist of at least 1 cat?
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Question 352189: In how many ways can a committee of 7 be formed if there are 10 dogs and 15 cats to choose from and the committee must consist of exactly 3 dogs and 4 cats?
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Question 352201: A survey of 51 pet owners revealed that 24 owned dogs, 28 owned cats, 11 owned turtles, 12 owned both dogs and cats, 7 owned both dogs and turtles, 3 owned both cats and turtles, and 2 owned all three. How many pet owners owned none of the following pets?
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Question 352428: How many possibilities are there for a jumble with 6 letter?
I tried this by doing 6x5x4x3x2x1=720 Did I do this right?

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Question 352428: How many possibilities are there for a jumble with 6 letter?
I tried this by doing 6x5x4x3x2x1=720 Did I do this right?

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Question 352450: The music class has 20 students & the teacher wants them to practice in groups of 5. How many different ways can the first groups of 5 be chosen? we are doing permutations & combinations. I came up with 1,860,480 or 38,760. im not sure which one is the right answer if any.
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Question 352458: A hamburger place has 25 different toppings. You can have a hamburger with upto 5 different toppings. Assume no toppings are used more than once, how many different choices are available? I did this by 25x24x23x22x21= 6,375,600 Did I do this right?
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Question 352464: A test consists of 15 true-false questions. In how many ways can the test be completed?
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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