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

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Question 1119790: In how many ways can a teacher arrange 10 students in the front row if there are 60 total students?
Click here to see answer by ikleyn(52781) About Me 

Question 1119789: How many ways can you purchase 5 CDs if there are 6 to choose from, 2 cassettes if there are 5 to
choose from, and 4 DVDs if there are 8 to choose from?

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Question 1119875: A bag contains 7 red marbles, 9 white marbles, and 9 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red? What is the probability that exactly two of the marbles are red? What is the probability that none of the marbles are red?
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Question 1120002: Toss a coin five times and observe the sequence of heads or tails. In how many of the sequence are the first three tosses identical?
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Question 1120002: Toss a coin five times and observe the sequence of heads or tails. In how many of the sequence are the first three tosses identical?
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Question 1120002: Toss a coin five times and observe the sequence of heads or tails. In how many of the sequence are the first three tosses identical?
Click here to see answer by MathTherapy(10552) About Me 

Question 1120103: Out of a group of 25 students,
7 walk to school, 12 catch a train
and 6 catch a bus. If 6 students
are selected, find the number of
combinations if 3 walk to school and
1 catches a bus.

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Question 1120189: a box contains a hundred rupee note,a ten rupee note, a five rupee note and four different coins. how many different amounts can be drawn from it.
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Question 1120190: a boy has 3 library tickets and 8 books of his interest in the library. of these 8, he does not want to borrow chemistry part 2, unless chemistry part 1 is also borrowed. in how many ways can he choose the three books to be borrowed?
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Question 1120191: out of 7 consonants and 4 vowels, how many words each containing 3 consonants and 2 vowels can be formed?
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Question 1120229: in how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the disc of same colour are indistinguishable?
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Question 1120228: a tea party is arranged for 16 people along two sides of a long table with eight chairs on each side. four particular men wish to sit on one side and two particular men on the other side.the number of ways they can be seated?
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Question 1120376: How many different signals can be sent up on a flagpole if each signal requires threethree blue and threethree yellow flags and the flags are identical except for​ color?

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Question 1120433: on your phone you have 23 rap songs and 14 country songs. How many 6 song playlists (order matters) can you make that have 4 rap and 2 country songs
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Question 1120544: A catering service offers
6 appetizers,
4 main courses, and
8 desserts. A customer is to select
2 appetizers,
3 main courses, and
3 desserts for a banquet. In how many ways can this be done?

Click here to see answer by Shin123(626) About Me 
Question 1120544: A catering service offers
6 appetizers,
4 main courses, and
8 desserts. A customer is to select
2 appetizers,
3 main courses, and
3 desserts for a banquet. In how many ways can this be done?

Click here to see answer by greenestamps(13200) About Me 

Question 1120676: A science test consists of 8 multiple choice questions, each of which has four possible answers. How many different ways can the 8 questions on the science test be answered?
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Question 1120764: A committee of 3 must be chosen from 8 candidates. What is the probability that certain three people will be selected?
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Question 1120813: A textbook search committee is considering 14 books for possible adoption. The committee has decided to select 4 of the 14 for further consideration. In how many ways can it do so?
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Question 364075: a boy have 5 coins each of different denominations. How many different sums of money he can form ? Its answer is 31 plz help
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Question 364075: a boy have 5 coins each of different denominations. How many different sums of money he can form ? Its answer is 31 plz help
Click here to see answer by greenestamps(13200) About Me 

Question 1121027: They are six kids they are celebrating their birthday, they are three boys and three girls, but they are each different ages. The youngest is 1 year old. The sum of the ages of the three girls is the same as the sum of the ages of the three boys. What is the smallest possible total of all six ages?
Click here to see answer by ankor@dixie-net.com(22740) About Me 
Question 1121027: They are six kids they are celebrating their birthday, they are three boys and three girls, but they are each different ages. The youngest is 1 year old. The sum of the ages of the three girls is the same as the sum of the ages of the three boys. What is the smallest possible total of all six ages?
Click here to see answer by Edwin McCravy(20055) About Me 

Question 1121073:
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Question 1121120: Can you help me solve this word problem please?: How many five digit numbers can be formed by using two 4s and three 6s?
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Question 1121121: Can you help me solve this word problem please?: A man bought two vanilla ice cream cones, three chocolate cones, four strawberry cones, and one pistachio cone for his ten children. In how many ways can he distribute the flavors among children?
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Question 1121121: Can you help me solve this word problem please?: A man bought two vanilla ice cream cones, three chocolate cones, four strawberry cones, and one pistachio cone for his ten children. In how many ways can he distribute the flavors among children?
Click here to see answer by greenestamps(13200) About Me 

Question 1121212: At a local cheerleaders’ camp, 5 routines must be practiced. A routine may not be repeated. In how many different orders can these 5 routines be presented?
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Question 1121222: Melanie has 4 different colored crayons and 2 different boxes as shown below. How many different ways can Melanie put all 4 crayons into the 2 boxes so that each box has at least 1 crayon?
Click here to see answer by solver91311(24713) About Me 
Question 1121222: Melanie has 4 different colored crayons and 2 different boxes as shown below. How many different ways can Melanie put all 4 crayons into the 2 boxes so that each box has at least 1 crayon?
Click here to see answer by ikleyn(52781) About Me 

Question 1120491:

Three research departments have 7,8 and 6 members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference. In how many ways can this be done?





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Question 1121344: Evaluate nP2+n+1P2
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Question 1120413: A catering service offers 5 appetizers, 3 main courses, and 12 desserts. A customer is to select 4 appetizers, 2 main courses, and 3 desserts for a banquet. In how many ways can this be done?
Click here to see answer by Boreal(15235) About Me 

Question 1121719: Prove that nCr=nCn-r
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Question 1121729: Find the value of n in the following;
8Cn = 4 x 7Cn

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Question 1121720:
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Question 1122110:
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Question 1122248: Luanne has seven frozen dinners -- two of them are the same kind of mushroom ravioli and the other five are the same kind of vegetable lasagna. Luanne is making plans to eat one of the dinners each day for the next seven days. How many different seven-day meal plans are possible?

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Question 1122247: Paige Turner loves finite mathematics. She has 4 books about probability and 3 books about matrices.
How many ways can she place these books on the same shelf in a row if:
a) there are no restrictions.


b) the books about probability are next to each other but the others could be anywhere on the shelf.


c) books are organized by their topic (probability books are next to each other and matrix books are next to each other).

Click here to see answer by math_helper(2461) About Me 

Question 1122447: Donna is merging the Bedford branch and the Spencer branch of her real estate agency. As a result, she must make some personnel decisions. She currently has seven employees in the two branches. She must select one of the seven to be the acting manager, two of them to be transferred to Indy, and one of them to be laid off. How many different ways could she do this?

Click here to see answer by ikleyn(52781) About Me 

Question 1122446: Luigi's Pizza has a very simple menu. They only sell pizza, and it only comes in one size. They don't have different varieties of crusts or sauces or cheeses. When you order a pizza, all you specify is which toppings, if any, you want on it. They offer eight toppings: sausage, pepperoni, mushrooms, onions, green peppers, spinach, pineapple, and anchovies. They do not allow duplicate topping orders; for example, you can't order a pizza with pepperoni and extra pepperoni.
How many different six-topping pizzas are possible at Luigi's Pizza?

How many different six-topping pizzas are possible if mushrooms must be one of the toppings?

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Question 1122451: How many ways can a team of fifteen hockey players choose a captain and two alternate captains?
Click here to see answer by ikleyn(52781) About Me 

Question 1122444: A standard deck of cards consists of four "suits" (clubs, diamonds, hearts,
and spades), with each suit containing thirteen cards of different "ranks"
(ace, 2 through 10, jack, queen, and king) for a total of fifty-two cards in
all. One often refers to the cards held by a player in a card game as their
"hand"; technically, a hand of cards can be thought of as a subset of the
deck of cards.
How many five-card hands are there that consist of exactly two queens and three kings kings?


Click here to see answer by Edwin McCravy(20055) About Me 

Question 1122445: Paige Turner loves finite mathematics. She has 5 books about probability and 4 books about matrices. Her friend Anita Tudor wants to borrow four of these books.
How many ways can Paige choose the books to lend Anita if:
a) there are no restrictions?

b) there are two books on each topic (i.e. two matrix books and two probability books)?

c) there is at least one book on each topic?

Click here to see answer by Edwin McCravy(20055) About Me 

Question 1122523: Let A = { a , b , c , d , e , f , g } . How many four element subsets of A do not contain the element a?
Click here to see answer by greenestamps(13200) About Me 

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