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

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Question 429803: you have a set of intergers 1-20 you make subsets of six numbers. Such that no one number is subsequet to the one before it(eg. 1,2...3,4..15,16..19,20 etcc)
good case (2,4,7,11,13,19)
bad case (1,2,4,11,14,17)
bad case (4,7,11,13,14,19)
the answer is 5005?
Click here to see answer by richard1234(7193)

Question 429907: How many different 15 persons committees can be formed each containing atleast 2 accountants and atleast 3 managers from a set of 10 accountants and 12 managers?
Click here to see answer by sudhanshu_kmr(1152)

Question 429911: In a fifteen question true false examination a student must acheive five correct answers to pass. If student answer randomly what is the probability that student will fail?
Click here to see answer by ewatrrr(24785)

Question 430132: There are 9 different positions on a baseball team. If a team has 16 players how many different line-ups can the team make?
Click here to see answer by sudhanshu_kmr(1152)

Question 430122: How many distinguishable words can be formed from the letters of the word "casserole" if each letter is used exactly once? If I told you the answer is 90,720; explain in your own words using complete sentences which formula you used and why (Permutations or Combinations), and how you solved the problem. When you state your answer here, please also tell us when the use of combinations is appropriate compared to when the use of permutations.
Click here to see answer by sudhanshu_kmr(1152)

Question 430300: In a certain coin-flipping game, the player wins if he/she gets an even number of heads in five tries. How many ways are there to win this game? (Note: 0 is an even number).

Click here to see answer by richard1234(7193)

Question 430898: how many different 7place licence plates are possible if the first 3 places are occupied by letters and the last 4 by numbers?
Click here to see answer by vleith(2983)

Question 430934: a collage planning committee consists of 3 freshmen, 4 sophomores, 5 junious and 2 seniors. a sub-committe of 4consists of 1 individual from each class. how many different sub committees are possible?
Click here to see answer by ewatrrr(24785)

Question 430922: Which lottery presents the player with the best odds for
winning, (A or B)? Defend your answer.

A = C(39,5)
B = C(40,4)

Click here to see answer by htmentor(1343)

Question 431526: How many ways are there to seat 4 people in a row of 6 chairs?
Click here to see answer by Edwin McCravy(20054)

Question 431670: determine the number of different passwords possible consisting of 5 different letters if the first letter must be a T and the 2nd letter is a C, and the 3rd letter is a U.
Click here to see answer by jorel1380(3719)

Question 431723: how many different ways can 5 people be seated on a bench if 2 of the people must sit next to eachother?
Click here to see answer by Edwin McCravy(20054)

Question 431823: 1) In how many ways can a class of 30 students choose 4 of their representatives?
2) How many elements in the sample space of drawing a card out of a standard deck of 52, tossing a coin, and tossing a 12-face die?
3) You are drawing two cards out of a standard deck of 52 cards, without replacing the first one back, what is the probability of you drawing a face then an eight card?
I have a question, how do you know when to use Permutations or Combinations? Both seem similar so it's hard to figure out which equation to use :[
Thanks so much !
Click here to see answer by sudhanshu_kmr(1152)

Question 432420: How many ways 20 oranges can be distributed among 3 kids?
Click here to see answer by ewatrrr(24785)

Question 432265: consider a political discussion group consisting of 5 democrats, 10 republicans, and 4 independents. suppose that two group members are randomly selected, in succession, to attend a political convention. find the probability of selecting two democrats.
Click here to see answer by sudhanshu_kmr(1152)

Question 432557: if 8 books are on a shelf, how many different ways can you group them?
Click here to see answer by ewatrrr(24785)

Question 432741: If there is a committee of 15 people, how many ways is there to divide it into 3 subcommittees of 3 people, 5 people, and 7 people.
Since order does not matter, i have tried 15C3*15C5*15C7 I am not getting the given answer of 360360 though...
Click here to see answer by edjones(8007)

Question 432996: Hello I need help : Use the binomial theorem to write the binomial expansion. (2x+5)^5. I don't understand how to do this.
Click here to see answer by ewatrrr(24785)

Question 432994: Find the number of possible 5-card hands that contain the cards specified. The cards are taken from a standard 52 dard deck.
A. 3 face cards and 2 cards that are not face cards. I have no idea what a face card is. I don't really play cards that often and know the terms.
Click here to see answer by shree840(260)

Question 432992: A baseball manager is determining the batting order for the team. The team has 9 players, but the manager definitely wants the pitcher to bat last. how many batting orders are possible??
Click here to see answer by htmentor(1343)

Question 432993: A pizza parlor runs a special where you buy a large pizza with 1 cheese, 1 vegetable, and 2 meats for $!2. You have a choice of 5 cheeses, 10 vegetables, and 6 meats. How many different variation of pizzas specials are possible?
For this one, I'm not sure, but I tried to multiple 5*10*6=300. However, I need help confirming if i did this problem right. Thanks.
Click here to see answer by sudhanshu_kmr(1152)

Question 432991: Find the nymber of possible 5 card hands that contain the cards specified. The cards are taken from a standard 52-dard deck. 5 red cards. I don't know what those are.
Click here to see answer by sudhanshu_kmr(1152)

Question 432988: A youth indoor soccer team has 6 starting players. The starting players must consist of 3 boys and 3 girls. there are 7 boys and 6 girls on the team. each player can play each position. In how many ways can the coach select players to start the game?
Click here to see answer by sudhanshu_kmr(1152)

Question 433152: A pizza shop offers 3 different toppings and 2 types of crust. How many possible types of pizza can you order if each pizza can have one, two, or three differnt toppings?
I got 78, but I think that is too many, because is pepperoni/ sausage the same as sausage/pepperoni????
I worked it out the long way (tree) and got 42 ???
Click here to see answer by stanbon(75887)

Question 433336: 6 digit passwords are randomly assigned to students by the computer department when they begin their freshman year. Assuming each digit comes from the set 0-9,
a. If no repetition is allowed, how many ways can the numbers be assigned?
b. What is the probablility that an assigned password will be 234567?
Thanks for your help!
Click here to see answer by jorel1380(3719)

Question 433416: Mr. Swanson is arranging chairs for the school band concert. The number of chairs in each row is a multiple of 6. Which of the following could be the number of chairs in each row?
Click here to see answer by stanbon(75887)

Question 433457: A test is given with 10 T-F questions. How many different ways can the answer sheet be filled out so that 8 or more questions are answered correctly? I am drawing a blank and do not know where to start?
Bob
Click here to see answer by jorel1380(3719)

Question 433458: My first questions is :
In how many ways can you answer the questions on the exam that consists of 6 multiple choice questions, each of which 4 answer choices, followed by 6 true-falso questions?
Second question :
Solve using permutations or combinations ;
A musician plans to perform 5 selections for a concert. If he can choose from 8 different selections, how many ways can he arrange his program?
Third Question :
Solve using permuations or combinations ;
There are 12 books on a reading list for English I. Students must select 4 books to read from this list. In how many ways can the 4 books be selected?
Fourth Question:
If Elizabeth eats dinner at home tonights, there is a 15% chance that she will eat dessert. If she eats dinner at a resaturant, there is a 60% chance that she will eat dessert. Suppose that there is a 55% chance that Elizabeth will eat oiut tonight. What is the probability that she will eat dessrt tonight?
Click here to see answer by sudhanshu_kmr(1152)

Question 433516: For a segment of a radio show, a disc jockey can play 6 records. If there are 10 records to select from, in how many ways can the program for this segment be arranged?
Click here to see answer by jorel1380(3719)

Question 433578: A four-digit number is formed from the digits 1, 2, 3, 4, 5, 6, and 7, with no repetitions. How many of these four digit numbers will have a number value between 1000 and 5000?
Click here to see answer by robertb(5830)

Question 433645: 1. A teacher chooses 4 students to attend a seminar. To do this, she chooses one boy and one girl from a class of 14 boys and 12 girls, and one boy and one girl from a class of 13 boys and 13 girls. In how many different ways can the teacher choose the 4 students? (That is, how many different gropus of 4 students can she created if she chooses one student from each of the four listed groups).
Hints:
Assume that the teacher chooses 1 boy from a group of 14, 1 girl from a group of 12, 1 boy from a group of 13 and 1 girl from a group of 13.
So there are 14 choices then 12 choices then 13 choices then 13 choices.

Click here to see answer by sudhanshu_kmr(1152)

Question 433627: How many ways are there to arrange the letters in the word permutation?

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Question 433646: 99 workers are finishing 634122 jobs in 7371 hours then how many hours required to finish 647437 jobs to 97 workers?

Click here to see answer by rwm(914)

Question 433646: 99 workers are finishing 634122 jobs in 7371 hours then how many hours required to finish 647437 jobs to 97 workers?

Click here to see answer by robertb(5830)

Question 433065: from a group of 5 men and 7 women, a committee of 2men and 3 women is to be formed. how many committees can be formed if 2 women are feuding and refuse to serve the community together?
Click here to see answer by sudhanshu_kmr(1152)

Question 433791: In Powerball, a player chooses 5 different numbers, the 5 white balls, from 1 through 49 and a single number, the red power ball, from 1 through 42. In how many ways can a player choose the numbers?
Click here to see answer by haleyw(1)

Question 434138: 12 people are on a basketball team and a coach needs to choose 5 to put into a game.How many possible ways can a coach choose a team of 5 if each person have a equal chance to be selected
Click here to see answer by Alan3354(69443)

Question 434318: Determine the number of 5-digit zip codes (assume the digits can be repeated, but the first digit cannot be zero).
Click here to see answer by edjones(8007)

Question 434554: a committee consisting of 6 members has to elect a president and a treasurer. in how many ways can they do this?
Click here to see answer by stanbon(75887)

Question 434605: How many different ways can the letters alaska be arranged
Click here to see answer by edjones(8007)

Question 435066: how many three card hands can be dealt from a deck of 52 cards
Click here to see answer by Alan3354(69443)

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