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

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Question 875227: In(3x+2)=3

Click here to see answer by ewatrrr(24785)

Question 875238: Using permutation,can you show me the number of ways the numbers 0-9 can be rearranged into groups of 4. My name is Andre and my email address is andre_easi@yahoo.com. I tried and I was gettting ten thousand but not too sure. Can you help please.
Click here to see answer by ewatrrr(24785)

Question 875356: In how many ways can seven books be arranged on a shelf if
a)the books are different and the mathematics book must be on an end?
b) the books are different and four particular books must be together?
Thank you!
Click here to see answer by jim_thompson5910(35256)

Question 875369: In how many arrangments can 5 women and 5 men be placed in a line if all men line up first?
-please show work
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Question 875259: you are playing cards and you draw a card from a pack of 94 cards numbered from 1 to 94. What is the probability of drawing a number that is a square?
Click here to see answer by KMST(5328)

Question 875414: A class has 15 girls and 19 boys. A committee is formed with two girls and two boys, each with a distinct responsibility. Determine whether this situation involves a permutation or a combination. Then determine the number of possible arrangements.
Click here to see answer by jim_thompson5910(35256)

Question 875417: How many even numbers of at least four digits can be formed using the digits 0,1,2,3 and 5 without repetitions? (Answer is 84)

Click here to see answer by Edwin McCravy(20054)

Question 875380: How many different 12-person committees can be selected from a pool of 24 people?
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Question 875472: Hello. I have a question regarding the number of combinations in the game Qwirkle. In Qwirkle, each chip has a shape and a color. There are six shapes and six colors, resulting in a total of 36 types of chips. There are three replications of each type. Thus, there are 108 chips in total. Six chips are initially drawn at random. So I am interested in finding the unique combinations of chips that can initially be drawn. Knowing this number will enable me to compute the probability of various outcomes. Here is the approach I took:
1) assume chips of the same type are indistinguishable (e.g. a blue square and another blue square are the same)
2) enumerate integer partitions with the restriction that the integers must sum to six and a single integer cannot exceed three (because there are only three of each type).
3) count the number of integers in each partition, K, and compute 36 choose K
4) sum the combinations from step 3
Partition 1: 3,3
Partition 2: 3,1,1,1
Partition 3: 2,1,1,1,1
Partition 4: 1,1,1,1,1,1
Partition 5: 2,2,2
Partition 6: 2,2,1,1
Partition 7: 3,2,1

Answer: 36 choose 2 + 36 choose 4 + 36 choose 5 + 36 choose 6 + 36 choose 3 + 36 choose 4 + 36 choose 3

Is my reasoning correct?
Thank you!

Click here to see answer by Edwin McCravy(20054)

Question 875415: Six students in a class meet in a room that has nine chairs. Determine whether this situation involves a permutation or a combination. Then determine the number of possible arrangements.
Click here to see answer by Edwin McCravy(20054)

Question 875676: How do I solve this question?
You own 9 travel books and are taking 4 on vacation. In how many ways can you choose 4 travel books from the total group.
I think it is 9C4, but don't know how to solve that
Click here to see answer by ewatrrr(24785)

Question 875373: How many distinct arrangements can be made with the letters in the word CINCINNATI
Click here to see answer by Edwin McCravy(20054)

Question 875075: How many arrangement are there of the letters in the word ANAGRAM if the arrangements cannot start with A?
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Question 875360: I will form a 6 letter code word using only the first 12 letters of the alphabet and allow repeated letters. If I select a code word at random find the probability that the code word has no vowels

Click here to see answer by Edwin McCravy(20054)

Question 875701: You found 25 books at the library but you can only check out 5. You have already chosen 2 books. How many different groups of five books can you have after the two you have already chosen?
Click here to see answer by Edwin McCravy(20054)

Question 875077: In backgammon, counters are placed on points marked by long triangles. You cannot land your counter on a point where your opponent has two or more counters, but you can jump over that point. How many rolls with two standard dice allow black to move past both white points in this position? Count (1,6) and (6,1) as different rolls.
Click here to see answer by Edwin McCravy(20054)

Question 875715: WHat is the value you of nCr when n= r+1?
Click here to see answer by jim_thompson5910(35256)

Question 874363: 1.Prove that 3^n=Summation(r=0,n)2^rC(n,r)
2. Evaluate summation(n=1,20)(1.1)^n
Click here to see answer by Edwin McCravy(20054)

Question 875820: The number of ways in which we can arrange 4 letters of the word mathematics is given by
Click here to see answer by jim_thompson5910(35256)

Question 875827: 5 keys can be arranged in a circular ring in what number of ways?

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Question 875911: How many different 6 card hands with at least 2 aces can be dealt from a standard deck of cards?
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Question 875910: In Oscar Wilde's play "The Importance of Being Earnest", there are 5 male roles and 4 female roles. However, one of the female roles, Lady Bracknell, is sometimes played by a male actor. Suppose 8 men and 6 women audition for a production of this play. After all the roles have been cast, _____different groups of unsuccessful auditioners are possible.
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Question 875907: The number of possible sequences of all the hearts from a standard deck, given that the ace and king cannot be next to each other and that the 13 cards are dealt in a single row, is __________________.
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Question 875935: There are 10 true / false question in an examination . Then these question can be answered in how many way
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Question 876109: how many ways can you arrange 9 pais of shoes in a row. the pairs stay together?
I tried 9*2=18*60=1080

Click here to see answer by josmiceli(19441)

Question 876220: In how many different ways a group of 7 students can be selected from a class 25 students
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Question 876591: How many different ways can 16 students be arranged in a line?

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Question 876609: There are 9 candidates running for 3 seats on a committee. How many different election results are possible? (1 point)
A)11
B)15
C)120
D)10

Click here to see answer by Alan3354(69443)

Question 876613: Evaluate C(9,7)
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Question 876576: how many passwords can you created with 2 letters (from 26 possible ones) followed by digits, if no letters repetition is allowed and the numeric part must have exactly one odd number?
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Question 876801: There are 6 children and husband/wife have to be in the middle. How many ways can they be seated?
Click here to see answer by jim_thompson5910(35256)

Question 877036: how is the choie of m
numbrer detemined
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Question 877119: A state's license plates consist of four letters followed by three numerals, and 240 letter arrangements are not allowed. How many plates can the state issue?
Click here to see answer by Edwin McCravy(20054)

Question 876821: Please solve for "r" algebraically, with all work shown: 7!/(r!(7-r)!)=35
Thank you!
Click here to see answer by Edwin McCravy(20054)

Question 877118: from a group of 5 boys and 4 girls, a committee of 4 must be selected. Each committee must have at least one boy and at least one girl. How many ways can this be done?
Thanks!
Click here to see answer by Edwin McCravy(20054)

Question 877133: Cut a circle into 8 congruent parts.
Use 4 colors to paint 7 parts of the circle.
The adjacent sides cannot have the same colors and you must use all 4 colors. How many methods are there?
Thank you so much.
Click here to see answer by Edwin McCravy(20054)

Question 877295: How many different four-person committees can be formed from a group of six boys and four girls?
Click here to see answer by richard1234(7193)

Question 877338: Which of the following numbers could be the probability of
an event?
1.5,1/2, 3/4,2/3,0 _ 1/4

Click here to see answer by Fombitz(32388)

Question 877669: 5-digit numbers are to be formed by using all the digits 0,1,2,3,4. How many numbers can be formed if the digits are allowed to repeat?
Click here to see answer by dkppathak(439)

Question 877821: in north Dakota, most license plates consist of 5 letters. How many different license plates are there if the letters can be repeated?
Click here to see answer by ben720(159)

Question 877727: if you have to choose a passcode that starts with 2 digits, 2 letters, then ends with either % or $ symbol, how many possible passcodes are there if the numbers and letters can be repeated?

Click here to see answer by Fombitz(32388)

Question 878149: if you tossed 2 nickles 100 times, how many times would you expect to get 200
Click here to see answer by Alan3354(69443)

Question 878136: A menu has 6 appetizers, 9 main courses, and 5 desserts. How many different meals are available if you choose an appetizer, main course and dessert?
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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