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

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Question 346757: In how many ways can someone pick 5 cubes out of 5 red and 5 orange cubes? Thank you.
Click here to see answer by jrfrunner(365)

Question 346765: how many different pairs can be made from 5 different items
Click here to see answer by nyc_function(2733)

Question 347117: Find the probability of a couple having a boy when their 6th child is born, given that the first five children were all boys. Assume boys and girls are equally likely. I'm not sure how to figure it out.
Click here to see answer by Fombitz(13828)

Question 347209: How many ways can you answer 15 true/false questions? i thought since there were 2 answers for every question thats 30 answers total so the final answer to the question would be 30 choose 15.
Click here to see answer by stanbon(57219)

Question 346835: 2 log 11 + 5 log 4
Using the Power Rule express as a single logarithm

Click here to see answer by nyc_function(2733)

Question 347881: A computer with an old processor locks up if more than 4 applications are running simultaneously. If the owner has 20 applications stored in his program file, how many different sets of 4 can he run, so that his computer does not lock up?
Click here to see answer by jim_thompson5910(28476)

Question 348117: How many arrangements of the letters in the word COUNTING are possible?

Click here to see answer by stanbon(57219)

Question 348507: In how many different ways can a panel of 12 jurors and 2 alternates be chosen from a group of 20 prospective jurors?
I tried C(20,12)*C(20,2) but that was wrong and i'm not sure how to do it, thanks
Click here to see answer by edjones(7569)

Question 348509: A student planning her curriculum for the upcoming year must select one of four business courses, one of four mathematics courses, two of six elective courses, and either one of five history courses or one of two social science courses. How many different curricula are available for her consideration?
The fact that she has to choose between either the history or the social science courses is why I cant figure it out
Click here to see answer by edjones(7569)

Question 348524: From a shipment of 60 transistors, 4 of which are defective, a sample of 4 transistors is selected at random.
(b) How many samples contain exactly 3 defective transistors?
(c) How many samples do not contain any defective transistors?

Click here to see answer by edjones(7569)

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.
Click here to see answer by stanbon(57219)

Question 349585: how many ways does 5 persons can seat in round table?
Click here to see answer by ewatrrr(10682)

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?
Click here to see answer by rfer(12644)

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?
Click here to see answer by stanbon(57219)

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

Click here to see answer by ewatrrr(10682)

Question 350208: A salad bar has 15 ingredient s . How many unique salads can be made?
Click here to see answer by jim_thompson5910(28476)

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?
Click here to see answer by ewatrrr(10682)

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?
Click here to see answer by jim_thompson5910(28476)

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.

Click here to see answer by stanbon(57219)

Question 350843: Find how many 3 digit numbers are even? Also find how many 4 digit numbers are composed of odd digits?
Click here to see answer by sudhanshu_kmr(1152)

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'.
Click here to see answer by sudhanshu_kmr(1152)

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
Click here to see answer by sudhanshu_kmr(1152)

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?
Click here to see answer by sudhanshu_kmr(1152)

Question 349185: Find the rank of MOTHER ? and also find the rank of BHARAT?
Click here to see answer by sudhanshu_kmr(1152)

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
Click here to see answer by sudhanshu_kmr(1152)

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
Click here to see answer by sudhanshu_kmr(1152)

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
Click here to see answer by sudhanshu_kmr(1152)

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?
Click here to see answer by sudhanshu_kmr(1152)

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?
Click here to see answer by sudhanshu_kmr(1152)

Question 347860: How many arrangements of the letters in the word COUNTING are possible?
Click here to see answer by sudhanshu_kmr(1152)

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?
Click here to see answer by sudhanshu_kmr(1152)

Question 342414: In how many ways can 12 poeple be divided into 3 groups of 4 persons(in each group)?
Click here to see answer by sudhanshu_kmr(1152)

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?
Click here to see answer by sudhanshu_kmr(1152)

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
Click here to see answer by edjones(7569)

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?
Click here to see answer by sudhanshu_kmr(1152)

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
Click here to see answer by sudhanshu_kmr(1152)

Question 347938:
In how many ways can a group of 4 boys and 4 girls be seated in a row of 8 seats?
Click here to see answer by sudhanshu_kmr(1152)

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?

Click here to see answer by sudhanshu_kmr(1152)

Question 348171: How many different ways can you seat 9 people in 4 chairs? I do not understand what equasion to use.
Click here to see answer by sudhanshu_kmr(1152)

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.
Click here to see answer by sudhanshu_kmr(1152)

Question 351383: how many words can be made by rearranging he letters in the word "minimum"?
Click here to see answer by user_dude2008(1861)

Question 351387: how many 9 letter words can be formed by permuting the letters of "territory"?
Click here to see answer by user_dude2008(1861)

Question 351393: in how many ways can a group of 6 people arrange themselves in a circle, holding hands for a group dance?
Click here to see answer by stanbon(57219)

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