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

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Question 992154: There are 4 letter boxes in a locality. In how many way can a man drop 3 letters into the letter boxes ?
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Question 991935: In how many ways can the letters A, B,C,D,E,and F be arranged for a six-letter security code?
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Question 991001: a circle is divided into five equal sectors with each sector orange, blue or green. the first sector must be orange. how many different pattern are there if adjacent sector are coloured differently
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Question 989986: how many numbers are there between 1000 to 10000 such that it is divisible by 6? ( give that no number repeat itself in the 4 digit number )
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Question 992416: How many odd numbers of four digits each can be formed with the digits 0,1,3,5,6 and 7 without repetition ?
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Question 993740: A card is picked from a standard deck of 52 cards, and then a coin is flipped 3 times. How many possible outcomes are there?
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Question 993839: An experiment consists of dealing 5 cards from a standard 52 card deck. What is the probability of being dealt a 5, 6, 7, 8, 9, all in the same suit?
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Question 993972: How many different 7-letter words can be made
A. if the first letter must be A, X or T and no letter may be repeated?
B. if repeats are allowed (but the first letter is A, X or T)?
C. How many of the 7-letter words (starting with A, X or T) with no repeats end in S?

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Question 993972: How many different 7-letter words can be made
A. if the first letter must be A, X or T and no letter may be repeated?
B. if repeats are allowed (but the first letter is A, X or T)?
C. How many of the 7-letter words (starting with A, X or T) with no repeats end in S?

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Question 993969: A game consists of asking 17 questions to determine a person, place or thing that the other person is thinking of. The first question, which is always, "Is it an animal, vegetable, or mineral?", has three possible answers. All other questions must be answered with "Yes or "No." How many possible objects can be distinguished in this game, assuming that all 17 questions are asked? Are 17 questions enough?
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Question 993968: A state lottery game requires that you pick 6 different members from 1 to 43. What is the probability of picking exactly 3 of the 6 numbers correctly?
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Question 993967: A container contains 15 diesel engines. The company chooses 7 engines at random, and will not ship the container if any of the engines chosen are defective. Find the probability that a container will be shipped even though it contains 2 defectives if the sample size is 7.
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Question 994001: If I had 5 different paints to paint my front and back door how many combinations can I make
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Question 994100: If the odds against an event happening are 81/55, what is the probability of the event happening?
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Question 994124: Two dice are rolled simultaneously. What is the probability of getting a sum of at least 4?
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Question 994009: find the permutation of number of ways in which 5 first year student and 5 second year student can be seated on a bench in a examination hall so that no two students of the same class are next to each other ?
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Question 994877: In a certain card game, players begin each round with 2 cards in hand, and then draw 5 more over the course of the round. If a player starts a round with 2 hearts, what is the probability that the player will have 5 or more hearts by the end of the round?
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Question 994958: how many 6 digit number can be formed without repeting any digit from the digit 0 1 2 3 4 5 6

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Question 994955: Grandma got a smart phone and needs help assigning the first four speed dial numbers to four of her 17 contacts. How many ways can the speed dial numbers be assigned?
Please show step by step

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Question 995031: Hello,
Let's say I have three letters; A, B and C. I need to know the formula how to count the number of all possible combinations using A, B and C, the letters can be repeated and the order of the letters is important (e.g. ABC and BCA are not the same).
All the way here I'm pretty confident I can solve this alone. 3%5E3 right?
Moving on, what if the number of digits can be 1, 2 or 3? (e.g. A, B, C, AA, AB, ..., AAA, AAB, ABC, ... )
Is there a way to count that any faster way than 3%5E3+%2B+3%5E2+%2B+3%5E1 ?
It is very time consuming if there can be any more than three digits in the answer and I have to manually solve it as shown above.
Thank you for your time!

Click here to see answer by rothauserc(4718) About Me 

Question 995519: An endurance contest is being held with two independent groups of 12 participants. Individual participants in the contest drop out before the end of the contest with probability 0.18 (independently of other participants). What is the probability that at least 11 participants complete the endurance contest in one of the two groups, but not in both groups?
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Question 995728: How many three digit even number can be formed then number is 0123456789
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Question 995681: How many 4-digit numbers greater than 1000 are there that use the four digits of 2012?
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Question 766872: 1. The Cool Gents is a R&B group planning their next concert tour. The band has a total of 25 new songs in their repertoire.
a. How many different set lists of 12 songs can the group select to play on tour? Use permutations or combinations. (Hint: the order of the songs is not relevant.)
b. How many different ways are there for the group to record a CD consisting of 12 songs chosen from 25 new songs? Use permutations or combinations. (Hint: The order in which the songs appear on the CD is relevant).

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Question 995962: Solve this: _+_+_=30 Fill the boxes using (1, 3, 5, 7, 9, 11, 13, 15) U can also repeat the numbers.
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Question 996827: In how many ways can a doubles game of tennis be arranged from six boys and eight girls if each side must have one boy and one girl?
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Question 997074: Three travelers arrived at a town where there are five hotels. In how many ways can they select their room each at a different hotels?
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Question 997223: How many permutations can be made from the letters of the word "WHITE" with vowels and consonants alternating?
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Question 997980: How many different 3-letter arrangements contain at least one R?
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Question 998085: In how many ways can nine students be selected randomly from a class of 40 students?
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Question 998094: How many ways can 2 men and 2 women be selected for a debate tournament if there are 14 male finalists and 13 female finalists?

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Question 998155: How many different ways can six types of laser printer be displayed on a shelf in a computer store?
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Question 997757: How to get 100 by using digits from 1 to 9. Rules-
Only addition can be used.......
every digit should and can used only once and compulsory to use every digit.........
pairs can be made like 2 and 3 digits can be used as 23 or 32........
Fractions can be used like 2 and 5 digits can be written as 2/5 or 5/2...........

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Question 997217: In the word "COMPUTER", there are 40320 distinct permutations. Among these permutations, how many of them:
a) begin with C and end with R?
b) begin with R and end with C?

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Question 997666: On an assignment, students are expected to answer at least 3 questions from a 16 question set. But they can complete as many questions as they wish (for bonus!). How many possible ways can they complete the assignment?
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Question 996826: Five prizes are to be given to five different people in a group of seventeen. In how many ways can a first prize, a second prize, a third prize and two fourth prizes be given?
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Question 998626: In how many ways can first, second, and third prizes be awarded in a contest with 110 contestants?
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Question 998679: _+_+_=30 use number 1,3,5,7,9,11,13,15
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Question 998763: A car painter charges £40 per day for himself and £10 per day for his assistant. If a fleet of cars were painted for £2000 and the painter worked ten days more than his assistant,how much did the assistant receive?
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Question 999128: The Computer Science department must select three faculty members to send to represent the department at a conference from the fifteen full-time faculty members. In how many ways can the selections be made?
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Question 999128: The Computer Science department must select three faculty members to send to represent the department at a conference from the fifteen full-time faculty members. In how many ways can the selections be made?
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Question 999128: The Computer Science department must select three faculty members to send to represent the department at a conference from the fifteen full-time faculty members. In how many ways can the selections be made?
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Question 999131: A student is applying for eight jobs in 8 separate states. All the interviews will require her to take flights to the destinations. She schedules her first interview in her home state of Florida and the last interview in Colorado. In how many ways can she arrange the interviews so she can do it all without returning home between any of the interviews?
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Question 999130: Each of three fraternities must each send two members to a meeting with the university administration. One fraternity has 20 members, another has 31 members and the third has 45 members. Determine the total number of ways in which these six people could be selected.
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Question 994856: --+--+--=30
Fill the boxes using (1,3,7,9,11,13)

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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