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

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Question 892181: I have three different types of nuts and four different types of nut cracker. The nut cracker can only crack one nut at a time. How many different possible ways can this be done?
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Question 892152: (n+1)!=42(n-1)! Find n
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Question 892187: please help me solve this problem.
a computer password made up of four characters. Each can be a capital letter (A-Z)a lower case letter (a-z) or a digit (0-9). if the password is randomly chosen, what is the probability that the password will only contain lower case letters? hint: use the multiplication rule to count the sample space and event space.
thank you =)

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Question 892188: use the alphabet 1,3,5,7,9,11,13,15
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Question 892216: How many six-symbol computer passwords can be formed using the letters A to J and the digits 4 to 6?

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Question 892342: In a train compartment, there are 8 seats, with 4 facing the front and 4 facing backwards. Find the probability that 2 particular people will sit opposite each other if seating is arranged at random.
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Question 892316: Given a set of N numbers, find the number of distinct possible sums that can be obtained by taking any number of elements from the N number of numbers and adding them.
this is a generalised question need to derive a general formula

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Question 892356: The sum of first 40 terms of the series 2+10+30+66+130........is
A)583210
B)615340
c)648620
d)673220

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Question 891919: How many combinations of 3 numbers are there in 23 numbers, when the order of each group doesn't matter?
EX: Group A would be 1,2,3 OR 2,3,1 OR 3,2,1 OR 1,3,2, etc... These would all be considered the same group.

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Question 888109: 1How many different ways may a row of on-off switches be set if no two adjacent switches may be off.
2 How many numbers can be made from the digits 2,3,4,5,6 if they are to be greater than 4000 and no repeats are allowed.

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Question 892503: In how many way can 12 similar balls be divided into 3 group with each group containing at most 6 balls
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Question 892184: Please help me solve this equation
1.Give your answer the following three questions in symbolic form, using the notation.
a. the board of directors of a company has 14 members. in how many ways can it choose a committee of three members? (where all members have equal standing)
b. 22 drivers start a race. assuming all of the drivers are equally skilled. how many top five finishes are possible?
c. how many different 3 topping pizzas can be made from a list of 20 different toppings?
Thank you =)

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Question 887456: A restaurant offers a lunch special with a soup, entree and drink. There are the same number of choices for each of these. How many of each must there be for a customer to order a different lunch special every day for 2 years?

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Question 886777: There are three brass house-number digits: 2, 3 and 5. How many distinct numbers can he formed using one, two, and three digits? Make a list of these distinct numbers.
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Question 892592: Please help..Decide whether you would use a permutation, a combination, or neither. Next, write the solution using permutation notation or combination notation, if possible, and, finally, answer the question.
A club with 30 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many ways can this be done?

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Question 892395: Classify the problem as a permutations, a combinations, or neither.
A student is asked to answer 11 out of 13 questions on a exam. In how many ways can she select the questions to be answered?(Order is not important).
(b) In how many ways can a chairperson and a vice chairperson be selected from a committee of 15 senators?
(c)How many permutations are there of the following word?
Combinatorics
(d) Tarot cards are used for telling fortunes, and in a reading, the arrangement of the cards is as important as the cards themselves. How many different readings are possible if four cards are selected from a set of eight Tarot cards?
(E)A state's license plate consist of four letters followed by three numerals, and 246 letter arrangements are not allowed. How many plates can the state issue?

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Question 892450: If a committee of 3 is to be chosen at random from a class of 13 students, what is the probability of the committee is to consist of a president, a vice president, and a treasurer?
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Question 892630: If a committee of 3 is to be chosen at random from a class of 13 students, what is the probability of the committee is to consist of a president, a vice president, and a treasurer?
I tried 1/286 and that was wrong.

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Question 892689: Find the number of ways of arranging the letters of the word CALENDAR in such a way that exactly 2 letters are present between L and D.
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Question 892685: consider the set A={a,b,c,d,e,f,g,h}. find the number of subsets of A which contain atleast 6 elements and include 'c' and 'e'.
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Question 892381: Evaluate the expression.
11p2

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Question 892694: Is this a trick question or does the 6 seats in the first row alter the answer?
In how many ways can 5 students from a class of 16 be arranged in the first row of seats. (There are 6 seats in the first row).
Help please.

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Question 892778: Evaluate the expression.
(a) (6)
(3)
(b) (10) (4) (3)
(6) (2) (1)

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Question 892927: a committee of 3 is to be formed from a group consisting of 5 men and 2 ladies. find the probability that(1) the committee does not include any lady (2)the committee includes both the ladies
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Question 892939: A shop has 8 different types of post cards and at least 12 of each type. How many selections of 12 postcards are there if
a) you can choose any number of each type?
b) you can choose at most one of type 1 and any number of the other types?

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Question 892937: An exam paper in mathematics contains 12 questions and students must answer 10 of them.
a) in how many ways can a student choose 10 out of the 12 questions to answer?
b) show, by using the extended pigeonhole principle, that if 200 students write the exam paper, then at least 4 students will choose the same 10 questions to answer. state clearly what the pigeons and pigeonholes are.

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Question 893406: Tom has 8 shirts, 3 pairs of jeans, and 4 pairs of tennis shoes. How many different outfits consisting of one shirt, 1 pair of jeans, and 1 pair of tennis shoes are possible?
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Question 893560: how many different license plates begin with two digits followed by two letters then three digits if none are repeated?

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Question 893814: A club has 49 members.

a) How many ways are there to choose four members of the club to serve on an executive committee?

[Num] ways

b) How many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office?

[Num] ways

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Question 893123: how many different readings are possible if three cards are selected from a set of seven tarot cards

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Question 894059: in a company, ID cards have 5 digit numbers.
a. can be formed if repetition of the digit is allow?
b. how many ID cards can be formed if repetition of the digit is not allowed.

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Question 894355: Solve this..
◻➕◻➕◻➕◻➕◻=30
Fill the boxes using (1, 3, 5, 7, 9, 11, 13, 15)
U can also repeat the numbers..
No empty boxes.

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Question 894373: how to make sum 30
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Question 894373: how to make sum 30
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Question 894432: how many gallons are in 108ml
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Question 894432: how many gallons are in 108ml
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Question 645715: Question from GRE PowerPrep II Practice Test #2
Quant section 3 of 5
Question 13 or 20
A certain identification code is a list of five symbols: S1,S2,D1,D2,D3. Each of the first 2 symbols must be one of the 26 letters of the English alphabet, and each of the last 3 symbols must be one of the 10 digits. Repeated letters and digits are not allowed.) What is the total number of different identification codes?

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Question 894461: In how many ways we can arrange the letters in the word 'MISSISIPI' so that all S's come together and 2 I's come together . the spelling of the word has been given like missisipi
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Question 894521: 7 people (4 boys and 3 girls) are available to play basketball. How many 5‐person teams can be made if
each team must have 3 boys and 2 girls?

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Question 881876: _+_+_+_+_=30
fill the boxes using(1,3,5,7,9,11,13,15) u can also repeat the numbers

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Question 881876: _+_+_+_+_=30
fill the boxes using(1,3,5,7,9,11,13,15) u can also repeat the numbers

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Question 894605: How many different digit numbers can be formed using the integers 1,2,3,4?
There are 8 letter boxes in a post office, In how many ways can a man post 4 distinct letters?
How many numbers of six digits can be formed from the digits 0,1,3,5,7,& 9 when no digit is repeated?
In how many ways can four boys & three girls be seated in a row containing seven seats if all three girls are together?


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Question 894655: the number of three digit numbers that can be formed in base 12 system?
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Question 894693: find the total number of selection of at least one red ball from a bag containing 4 red balls and 5 black balls; balls of the same colour being identical?
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Question 895160: 3 ladies and 3 gents can be seated at a round table sothat any two and only two of ladies sit together number of ways is?
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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