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

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 Algebra: Combinatorics and Permutations Solvers Lessons Answers archive Quiz In Depth

 Question 56961: Can someone, please, explain why this equation is true? I intuitively understand why it works for odd n (as combinations with k elements are as many as combinations with n-k elements and they just cancel each other out in the end). But this doesn't explain the equation for even n. Thanks! Click here to see answer by stanbon(57246)
 Question 56961: Can someone, please, explain why this equation is true? I intuitively understand why it works for odd n (as combinations with k elements are as many as combinations with n-k elements and they just cancel each other out in the end). But this doesn't explain the equation for even n. Thanks! Click here to see answer by fanks(6)

 Question 55651: I really don't know how to go over this. I am confuse about the linear triplet part.Please explain...Thanks. DNA (Deoxyribonucleic acid) is made of nucleotides, and each nucleotide can contain any one of these nitrogenous bases: A(Adenine), G (Guanine), C (cytosine), T(thymine). If one of these four bases(A,G,C,T) must be selected three times to form a linear triplet,how many different triplets are possible? Note that all four bases can be selected for each of the three components of the triplet. Click here to see answer by fanks(6)

 Question 57067: if 18c2r=153*13c2r-5 what is the value of r? Click here to see answer by tutorcecilia(2152)

 Question 58680: I don't know how to solve this I don't understand what this is asking me to do. Can you show me how to set this up? P(6,5) Click here to see answer by checkley71(8403)

 Question 59432: An election committee of three men and four women has been formed to elect a local representative. Each of the seven members must be assigned to investigate one of seven different candidates. How many different ways can those assignments be made? Click here to see answer by aaaaaaaa(138)

 Question 59433: An election committee of three men and four women has been formed to elect a local representative. Each of the seven members must be assigned to investigate one of seven different candidates. How many different ways can those assignments be made? so do I just plug 4 into the combination formula and then 3, which both give me 35, and then multiply 35*35? do I have todivide that answer into 49 which is the 7 times 7? I am confused. Click here to see answer by aaaaaaaa(138)

 Question 59864: I do not understand how to tell when to use combination and when to use permutation. The word problem is: Jack has seven frozen meals in his freezer. How many ways can he choose to have them for dinner Sunday through Saturday? Click here to see answer by funmath(2925)

 Question 59891: Find the first five outputs of the following recursively defined function: f(1)=8,(thats given) f(n+1)=-f(n)+6 its not really a permutation but i didnt know what category to put it in Click here to see answer by stanbon(57246)

 Question 61819: 5 School children, including L & M, will be seated in a row of 5 seats. In how many ways can this be done id L & M must NOT sit together? I tried 5! (# of ways 5 can sit together) - 4! (if L & M did sit together). Please help. Click here to see answer by stanbon(57246)

 Question 62107: can you plaese help and explain if you would like, solve this equation? please 7/x + 1/2 =4 Click here to see answer by rchill(405)

 Question 62106: can you plaese help and explain if you would like, solve this equation? please 7 1 - + - = 4 x 2 Click here to see answer by rchill(405)

 Question 62971: Richard Stanley writes in his book "Enumerative Combinatorics" that it is easily seen why where f(n) is the number of subsets of [n] ({1,2,3,..,n}) that do not contain two consecutive integers. Can someone actually explain why it is so, please? Thanks! Click here to see answer by joyofmath(189)

 Question 63104: I hope you can help me with this problem: A ski trip at the school has been arranged. There are 30 students that have paid for the trip and 6 parnts that have volunteered to chaperone. To transport the students and parents easily they are to be divided into two groups. One group has 10 students and 2 parents, and the other group has 20 students and 4 parents. A) How many different groups of ten students can be formed? B) How many diffeent groups consisting of 10 students and 2 parents are posible? C) Kelly is one of the students going on the trip, and Kelly's mother is a chaperone. Kelly's mother would prefer to be in the smaller group and not in the same group as Kelly. If this wish is honoured, how many ways can the smaller group and its chaperone be chosen? Click here to see answer by stanbon(57246)

 Question 63762: This was an extra credit question that nobody knew how to answer. We have not covered permutations and could find nothing about it our books. Please help: How many permutations of the word PRODUCT are there, if all the letters are used without repetition. Click here to see answer by joyofmath(189)

 Question 63950: An urn contains 8 white balls and 4 red balls. In how many ways can 4 balls be drawn if a) 3 balls are white an 1 is red b) 2 balls are white and 2 are red c) all four balls are white Click here to see answer by stanbon(57246)

 Question 64542: Balls numbered 1 to 12 are dropped from the top of a maze, flow thru and land in slot A, B, C and D. In how many ways can the ball land if a)5,3,1,3 balls fall into A, B, C and D b)an equal number of balls fall into each slot and c) two slots are empty and an equal number of balls fall into the other two slots? I think that part a) 12!/5!3!1!3! and b) 12!/4.3! are these ok? please help with part c. Click here to see answer by stanbon(57246)

 Question 65318: a bag contains five green marble and three red marbles. if three marbles are chosen at random without replacement, what is the probability that all three will be green? Click here to see answer by stanbon(57246)

 Question 65320: 1)a commitee of 5 is to be chosen from men and 3 women. what is the probability that the commiteee will include all 4 men? 2) mrs. young teaches 10 boys and 15 girls in her algebra class. she chooses two students at random to work on the blackboard. a) how many different four member teams are possible? b)how many of these team will consist of exactly two juniors and two sisters? c)what is the probability that one of the four member teams will consist of exactly one juniors and three seniors? d)what is the probability that one four member team will consist of juniors only? Click here to see answer by stanbon(57246)

 Question 65417: Ten teams play a game in which they either win lose or draw. With a key of W=win L=Lose and D= Draw - I suppose the first permutation would be WWWWWWWWWW, perhaps followed by WWWWWWWWWL etc etc. ...What would the total number of permutations be for all ten games. Is it possible to see all the possible permutations for this online? Click here to see answer by stanbon(57246)

 Question 66198: Karen has forgotten the four-digit code to activate the copying machine. She remembers the digits are 2, 4, 5, and 6. How many possible combinations are there for Karen to try? Click here to see answer by Nate(3500)

 Question 66200: I learned this last year, but I don't remember the formula and I can't find it anywhere. I appreciate any help!! A store sells 5-cent, 10-cent, and 15-cent pencils. How many different ways can you spend \$.45 on pencils? Click here to see answer by checkley71(8403)

 Question 66432: how do you know exactly when the problem is a combination or a permutation? how do you label the problem? ex. 4 super script c 3? how do you solve these? Click here to see answer by stanbon(57246)

 Question 66971: When the binomial (2x-3y)^11 is expanded, what is the coefficient of x^8y^^3 taking into consideration the coefficients 2 and -3. Thank you Click here to see answer by stanbon(57246)

 Question 67160: How many 5 digit numbers can be formed from the numbers 1 to 7 with repeating a number? There are 15 community members campaigning for seats on the town council. If there are only five open seats, how many different ways can the community members be elected? Click here to see answer by stanbon(57246)

 Question 67428: how to determine order of permutation? with examples. Click here to see answer by prabhjyot(164)

 Question 68165: Six people are running a race. How many arrangements of winner, second place, and third place are possible? A 18 B 36 C 108 D 120 Click here to see answer by stanbon(57246)

 Question 68166: There are 9 players on a softball team. How many ways can the coach pick the first 5 batters? A 5 B 45 C 15,120 D 72,876 Click here to see answer by stanbon(57246)

 Question 68461: 3 girls & 4 boys are to be seated in a row containing 7 chairs. If the chairs at both ends of the row must be occupied by girls, in howmany different ways can the children be seated? Click here to see answer by checkley71(8403)

 Question 68455: In how many ways can 7 different colors be arranged in a row if the first is always red, the last is always blue and the middle one is always green? Click here to see answer by checkley71(8403)

 Question 68971: a= (2, 3, 4) & b= (3,4,5) solve a u b A upisde down u b Click here to see answer by funmath(2925)

 Question 69055: Given the digits 3,9,5,6& 2, howmany different 5 digit numbers reater than 41,000(using each digit once) can form? Click here to see answer by josmiceli(9661)

 Question 69034: Each Morse code symbol for a letter of the alphabet consists of dots(.) and dashes(-). Each symbol contains between 1 and 4 dots or dashes. How many different symbols can be made. Click here to see answer by josmiceli(9661)

 Question 70054: Replacement times for new Ford Taurus GL automobiles are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years. Find the probability that seven randomly selected Taurus GL automobiles will have a mean replacement time greater than 7.0 years. get z=.071 a=4721 and .5279 Click here to see answer by stanbon(57246)

 Question 70124: if you invest \$100 at the end of each month in a fixed-interest mutual fund paying annual interest of 6% compounded monthly, how much will your investment be worth after 10 yrs? Click here to see answer by stanbon(57246)

 Question 70126: this term there are eight candidates for three student senate seats, how many different ways can the seats be chosen? Click here to see answer by stanbon(57246)

 Question 70125: twelve students are in a class. they are split so that five go to room A, four go to room B and three go to room C. how many different ways can this happen? Click here to see answer by stanbon(57246)

 Question 70123: Permutations are just an application of fundamental counting principle. Combinations are just a application of Permutations and the counting principle. So would you say that Combinations are also just an application of the counting principle? Click here to see answer by stanbon(57246)

 Question 70262: A die is rolled. The sample space of equally likely outcomes is {1,2,3,4,5,6} find the probability of getting 9 Click here to see answer by checkley75(3666)

 Question 70264: You have six pairs of jeans, three shirts, two pairs of sandles. How many different outfits can you wear from these choices? Click here to see answer by checkley75(3666)

 Question 71406: find the number and sum of all the divisor of 840 Click here to see answer by venugopalramana(3286)

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