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

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Question 611961: How many solutions does the equation x1+x2+x3=8 have such that x1,x2, and x3 are integers, x1 ≥ 1, x2 ≥ 0, x3 ≥ 2.
Click here to see answer by richwmiller(9137)

Question 611967: please help.
Katarina has nine pairs of shoes to arrange in her closet. Assuming that she doesn't separate the pairs, how many different arrangements can she make?
Click here to see answer by richwmiller(9137)

Question 612005: a student is asked to answer 8 out of 10 questions on exam. How many ways can a queston be answered?
Click here to see answer by solver91311(16885)

Question 612007: A club with 34 members is to select 5 officers ( president, vice president, treasure, secretary, historian) In how many ways can this be done?
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Question 611995: how many ways can 10 books be arranged on a bookshelf
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Question 611998: a lock has 3 tumblers and each tumbler can assume 5 positions. how many different possibilities are there.
Click here to see answer by rfer(12660)

Question 612059: How many different ways can three CDs be chosen from a case of 10 CDs?
Click here to see answer by richwmiller(9137)

Question 612094: how many ways can five airplanes be arranged on a runway?
Click here to see answer by jim_thompson5910(28595)

Question 612173: How many arrangements of the word CHORD can be made that begin with either an H or an O?
Click here to see answer by richwmiller(9137)

Question 612215: A bookself has space for 6 books. If 8 different books are available, how many different arrangements can be made on the shelf?
My answer was 28. I found this by using the following combination:
(8 nCr 6) = 28
I was marked wrong, what is the correct way to do this problem and how can i avoid this mistake in the future?
Click here to see answer by stanbon(57352)

Question 612196: The contractor wants to plant six oak trees, nine maple trees, and five poplar trees along the subdivision street. The trees are to be evenly spaced. In how many distinguishable ways can they be planted?
I got this far:
20!/(6!9!5!) = 77,597,520
I need to know the break down of this equation to get the answer.
Click here to see answer by Edwin McCravy(8909)

Question 612345: how many different 5 player teams can be made from a group of 12 people?
Click here to see answer by alicealc(281)

Question 612337: If you guess on three multiple choice questions where A,B,C,D are the only options, what are your chances of getting those three answers correct.
Click here to see answer by flame8855(424)

Question 612429: how do you write 1/10 of a centimeter in decimals
Click here to see answer by Alan3354(30993)

Question 612429: how do you write 1/10 of a centimeter in decimals
Click here to see answer by lynnlo(4164)

Question 612566: what is the probability of meeting either a boy or chess player where there are 12 boys in chess, 6 girls in chess, 8 boys not in chess, and 20 girls not in chess?
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Question 612563: Suppose f(x) = x2 + 6x - 91 and g(x) = . At which of these points does the function (fxg)(x) have a hole?
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Question 612577: A student is asked to answer 7 out of 9 questions on an exam,in how many ways can she select the questions to be answered
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Question 612575: what is 8P3? but the numbers should be little on the bottom.
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Question 612592: evaluate the expression (9/3)(4/3)(4/1)
Click here to see answer by rfer(12660)

Question 612768: Hi Team ,
Please help me here ,

i have a requirement that , i need to generate 8 digit word [mix of 26 small letters and 0-9 digits , both are repeatable]
Please give me the count of such words we can generate , Please let me know the probability to repeat the same word twice

Thanks
Kiranreddy.
Click here to see answer by Alan3354(30993)

Question 612955: How many different 10 letters word (real or imaginary) can be formed from the following letters TPIOOYPUTM
______ten letter words (real or imaginary can be formed with the giver letters.
Click here to see answer by ewatrrr(10682)

Question 613081: The code for a lock consists of 5 digits. The last number cannot be 0 or 1. How many different codes are possible?
Six different books will be displayed in the library window. How many different arrangements are there?
The three best essays in a contest will receive gold, silver, and bronze stars. There are 10 essays. In how many ways can the prizes be awarded?
In a talent show, the top 3 performers of 15 will advance to the next round. In how many ways can this be done?

Click here to see answer by solver91311(16885)

Question 613117: Yves and some friends are playing a fair game in which 18 cards are dealt to 6 players. One of the cards is a queen. The player who receives the queen goes first. What is the probability that Yves will go first?
a) 1/18 b) 1/3 c) 1/6 d) 1/13
Click here to see answer by solver91311(16885)

Question 613190: Hi,
How many combinations of numbers from 2 through 15 can be created from a base of 3000 numbers? I keep maxing out my calculators (and brain) with this. Exponential answer is preferred.

A practical way to look at this is to think of something like 3000 genes and how many possible combinations linking as few as 2, and as many as 15 genes in a string.
Thanks!
Click here to see answer by scott8148(6628)

Question 613252: There is a combination lock with 4 numbers, 2 of the numbers must be: 1, 2 or 3 and the other 2 numbers must be: 6, 7 or 8. Write an equation to show the total number of combinations.
Click here to see answer by stanbon(57352)

Question 613316: (9,5)(5,3)(4,1)Evaluate the expression.

Click here to see answer by Alan3354(30993)

Question 613394: Your classes are being scheduled for the upcoming school year. You will be taking English, Math, History, PE, Spanish, Woodshop and Computer. What is the probability that Workshop will be scheduled during 1st period and Math during 2nd period?
Click here to see answer by stanbon(57352)

Question 613523: 4 cards are drawn from an ordinary deck. In how many ways is it possible to draw 3 cards of the same suit?
Click here to see answer by edjones(7569)

Question 613650: Approximately 80% of American households have a computer. 9 households are randomly selected.
a) What is the probability at least 6 households have a computer?

b) What is the probability at most 3 households have a computer?

A stockbroker gains 3 new accounts, on average, in a week’s time. What is the probability that he gains 15 new accounts in the next 4 weeks?

Click here to see answer by ewatrrr(10682)

Question 613749: How many ways can a president and a vice president be selected in a class of 25 students
Click here to see answer by jim_thompson5910(28595)

Question 613749: How many ways can a president and a vice president be selected in a class of 25 students
Click here to see answer by ewatrrr(10682)

Question 613909: Any four people on a committee of seven people can make a decision for the committee. How may groups of four people are there.
I am reallyngood at math but this chapter just doesnt make sense to me. I get A's on all the assignments but it takes forever for.me to get the right answer. Please help. This is what i attempted to do.
7*6*5*4/4*3*2*1 with an answer of 35
Click here to see answer by stanbon(57352)

Question 613900: A computer password consists of 3 different digits followed by one of the letters A, B, C, D, or E. If the first digit of the password cannot be a zero, then the number of different passwords possible is?
Click here to see answer by stanbon(57352)

Question 614065: In the Word Pencils, how many combos can you make if the "N" has to be the first letter and P and I have to be next to each other.

Click here to see answer by stanbon(57352)

Question 614397: how many different 6 member teams can be chosen from a group of ten students to participate the next month in the math competition, ifeach student hasan equal chance of being chosen
Click here to see answer by vleith(2825)

Question 614921: There are 20 students in a class, 10 who are girls, and 10 who are boys. The teacher is choosing 4 of these students to be on a committee. What is the probability that there will be at least one girl and at least one boy? Use complementary counting.
Click here to see answer by stanbon(57352)

Question 614919: How many different teams can be organized consisting of 2 men, 2 women and 2 children? We have the following groups available for team assignments: 6 men, 5 women and 4 children.
Click here to see answer by ashipm01(26)

Question 614930:
Given P(A), find P(not A).
P(A)=98%
Click here to see answer by ashipm01(26)

Question 615071: a student is asked to answer 11 out of 15 questions of a exam. In how many
ways can she select the questions to be answered?
Click here to see answer by math33(31)

Question 614699: in how many different ways can a president, treasurer, and secretary be appointed rom a committee of 5 people?
Click here to see answer by math33(31)

Question 615304: A four digit number is to be formed from the digits 1, 3, 5 and 8. What is the probability that the number so formed will:
a) start with 5?
b) be an odd number? and
c) be greater than 5000?
Click here to see answer by stanbon(57352)

Question 615596: A 5 disc CD player randomly chooses the order in which to play the discs. How many ways can the CD player select the discs?
Click here to see answer by stanbon(57352)

Question 615594: If there are 16 girls and 10 boys in a class, how many ways are there to select a girl and then a boy?
Click here to see answer by stanbon(57352)

Question 615815: A class has 10 boys and 12 girls. Find the probabliltity of selecting a committee of four with at most two girls? I have the answer, which is 4620/ 7315. I got 7315 by doing 22C4. How do i get 4620?
Click here to see answer by scott8148(6628)

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