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

Tutors Answer Your Questions about Permutations (FREE)

Question 388973: Find the number of ways the letters of each word can be arranged. The word is "ALBUQUERQUE" I got 1,663,200. But it seems wrong. D:
Click here to see answer by haileytucki(390)

Question 388756: 6 people will sit in pairs on 3 benches. How many possible ways can they be arranged?
Like.
1 2 and 3 4 and 5 6 = 1 way
1 2 and 4 3 and 5 6 = 2 ways
1 2 and 3 4 and 6 5 = 3 ways
1 3 and 2 4 and 5 6 = 4 ways
Click here to see answer by sudhanshu_kmr(1152)

Question 388457: I. Seven letter words are formed using the letters of the word BLACKER.
(a)How many which end in R? (b)How many in which E immediately follows K?
(c)How many do not begin with B?(d)How many in which the vowels are separated by exactly two letters? (e)How many in which the vowels are seperated by two or more letters?
I really appreciate any help
Click here to see answer by sudhanshu_kmr(1152)

Question 389176: Please help me solve this question.

You are in charge of a company that is about to bring its new product to market. Here are your choices: select a large, medium, or small market; then launch, license out, or sell rights to the product.
How many choices do you have?

Click here to see answer by robertb(5830)

Question 389187: Please help me solve this problem.

How many distinct arrangements can be made with the letters in the
palindrome �Madam I�m Adam�? (Disregard the apostrophe and
capitalization.)

Click here to see answer by stanbon(75887)

Question 389371: in how many ways we can form a commitee of 5 person,form a group of six men and four women,which has atleast 3 women

Click here to see answer by robertb(5830)

Question 389396: there are 12 yes/no types of questions ,in how many ways can they be answered?

Click here to see answer by Alan3354(69443)

Question 389541: season greetings!
this is the question:
Suppose you are making a bracelet with all different colours and shapes of beads. How many bracelets are possible if you use:
a) 4 beads?
b) 5 beads?
c) 6 beads?
d) N beads?
Click here to see answer by robertb(5830)

Question 389443: Please help! I don't understand where to begin the problem and the "at least one male student" is confusing me!!
Problem:
You are attending two classes this summer. Suppose the first class has 28 students and second class has 25 students. There are 15 females in the first class and there are 12 males in the second class. How many different ways could you select two groups of 3 students (one from each class) so that in each group you must have at least 1 male student?

Click here to see answer by sudhanshu_kmr(1152)

Question 389512: Find the sum of all four digit numbers that can be formed using the digits 1,2,3,4,5, each digit appearing at most once.
Click here to see answer by robertb(5830)

Question 390475: How many 4-letter words with at least one vowel can be constructed from the letters A, B, C, D, and E?
Click here to see answer by haileytucki(390)

Question 390475: How many 4-letter words with at least one vowel can be constructed from the letters A, B, C, D, and E?
Click here to see answer by sudhanshu_kmr(1152)

Question 390475: How many 4-letter words with at least one vowel can be constructed from the letters A, B, C, D, and E?
Click here to see answer by richard1234(7193)

Question 390478: There are 2 girls and 7 boys in a math club. A team of four persons must be chosen for a tournament, and there must be at least 1 girl on the team. In how many ways can this be done?
Click here to see answer by stanbon(75887)

Question 390476: In how many ways can 7 people be seated in a row of chairs if two of the people, David and Becky, refuse to sit together?
Click here to see answer by robertb(5830)

Question 390312: a teacher gives 5 objective type questions out of which 4 have to be answered what are the total number of ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices
Click here to see answer by robertb(5830)

Question 390864: In how many ways can a ballot be validly marked if a citizen is to choose one of three candidates for mayor, one of four for city councilwoman, and one of three for district attorney. A citizen is not required to vote for all three positions, but he is expected to vote for at least one.
Click here to see answer by solver91311(24713)

Question 390865: How many 5-digit numbers have at least one zero?
Click here to see answer by richard1234(7193)

Question 390865: How many 5-digit numbers have at least one zero?
Click here to see answer by solver91311(24713)

Question 390858: Signals are made by running five colored flags up a mast. How many different signals can be made if there is an unlimited supply of flags of seven colors?
Click here to see answer by stanbon(75887)

Question 391045: how many ways can 3 students be picked from a group of 5
Click here to see answer by solver91311(24713)

Question 391110: How many different ways of order can four objects be lined up?
Click here to see answer by solver91311(24713)

Question 391110: How many different ways of order can four objects be lined up?
Click here to see answer by jim_thompson5910(35256)

Question 391110: How many different ways of order can four objects be lined up?
Click here to see answer by rfer(16322)

Question 391380: How many ways can six different books be arranged on a shelf if one of the books is a dictionary and it must be on an end?
Click here to see answer by sudhanshu_kmr(1152)

Question 391305: If I choose a password consisting of 3 letters & 3 numbers, and the first letter must be from the first half of the alphabet, the last number must be even and no repetition is allowed, how many passwords are possible?
Click here to see answer by sudhanshu_kmr(1152)

Question 391588: In how many ways can you arrange the letters of the word 'think' so that the 't' and the 'h' are separated by at least one other letter? Use the indirect method.
Click here to see answer by edjones(8007)

Question 391823: In how many ways may 6 students be seated in a row of 9 seats?
Click here to see answer by stanbon(75887)

Question 391824: How many different signals can be made from 6 different flags if each signal is to consist of 3 flags hung in a horizontal row?
Click here to see answer by stanbon(75887)

Question 391824: How many different signals can be made from 6 different flags if each signal is to consist of 3 flags hung in a horizontal row?
Click here to see answer by sudhanshu_kmr(1152)

Question 391827: In how many ways can a committee of 5 people be formed from a group of 10 if certain 3 men insist on serving together or not at all?
Click here to see answer by richard1234(7193)

Question 391826: How many sums of money, each involving 3 coins, can be formed from a penny, a nickel, a dime, and a quarter?
Click here to see answer by Edwin McCravy(20054)

Question 392048: The number of students divided equally into four teams
Click here to see answer by stanbon(75887)

Question 392151: prove that P(n,n) = 2P(n,n � 2)
and prove that C(2n,2) = 2C(n,2) + n^2 .

Click here to see answer by robertb(5830)

Question 392603: how many different 4-digit numbers can be formed from th digits 2, 3, 4,5,6,7,and 8 if:
a)repetition of digits is not allowed?
b)repetition of digits is allowed?
c)how many of them are odd numbers? refer to (a).
d)how many of them are even numbers? refer to (b).
Click here to see answer by sudhanshu_kmr(1152)

Question 392595: There are 3 mangoes, 4 Guava & 5 oranges.In how many ways can they be arranged in a row.
Click here to see answer by sudhanshu_kmr(1152)

Question 392402: our companys id cards consist of 3 letters followed by 2 numbers. how many cards can be made if repetitions are allowed?
Click here to see answer by sudhanshu_kmr(1152)

Question 392593: find the total no. of numbers less then 1000 & divisible by 5 that can be formed with the digits 0,1,2,3,4,5,6,7,8,9(none of the digits repeated).
Click here to see answer by sudhanshu_kmr(1152)

Question 392597: In how many ways can the letters of the word ALLAHABAD be arranged so that the vowels can occupy only even positions.
Click here to see answer by sudhanshu_kmr(1152)

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