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

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Question 293969: How many numbers less than 10000 can be made with the eight digits 1,2,3,0,4,5,6,7
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Question 294652: how many arrangements of answers are possible for a true/false test with 10 questions
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Question 294707: For a visit to the municipal library, a teacher asks her students to form rows of 3 students per row. Solène, Nadine and Yasmine are in the 5th row starting from the front and the 6th row starting from the back. How many students will visit the library?

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Question 294869: 15 women can knit 6 sweaters in 20 days working 6 hours a day. Find in how many days can 20 women knit 10 sweaters working 3 hours a day?
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Question 295798: How many ways can you arrange the letters in the word GROUP?
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Question 295810: How many different 4-digit numbers can be created if no digit can be repeated? Remember, a number cannot begin with 0..
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Question 295952: A theater contains 25 rows of seats. The first row contains 25 seats. Each succeeding row has one more seat than the row immediately before it. How many seats does the theater have?

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Question 296502: How many different ways can a college select three applicants for a teaching position from a pool of 20 applicants.
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Question 296855: Consider a political discussion group consisting of 9 Democrats, 4 Republicans, and 7 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting an Independent and then a Democrat.
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Question 298289: If any two points determine a line, how many lines are determined by seven points in a plane, no three of which are collinear?
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Question 298295: How many triangles are determined by
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Question 298292: How many triangles are determined
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Question 298290: How many triangles are determined by 20 points in a plane, no three of which are collinear?
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Question 299498: How many three-digit numbers can be formed under the following conditions?
(a) The leading digit cannot be zero
(b) the leading digit cannot be zero and no repetition of digits
(c) the leading digit cannot be zero and the number must be a multiple of 5
(d) the number is at least 400
for (a) i tried doing 9^3 which gives me 729, the ans. in the back of the book says 900, i also tried doing 9 nCr 3 which gave me 85, and 9!/3!

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Question 299611: how can i solve 26c14 when 26 is a very large number?
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Question 299623: Phone numbers are seven digits long and the digits an repeat themselves. Using this information, find the probability for when the phone number ends with an even digit. Thank you for your help.
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Question 300108: how many ways can a hand of five cards consisting of three cards from one suit and two cards from another suit be drawn from a standard deck of cards?
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Question 300443: How do you solve this problem using numbers not words
how many ways can 5 children line up to get on the bus if Jenny always gets on third

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Question 300430: Is this problem solved using Permutations or combinations.
How many ways can a club of six members choose a 3 person committee?

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Question 300415: What is 7 permutation 3. And 7 combination 3??
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Question 301724: How many 3-digit numbers greater than 400 can you make using the numbers 2, 1, 4 and 3 only once each time?
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Question 301684: How many ways can you line up 8 children in order if Sally has to be separated from both Mary and Jan?
*I know to get the total amount of options for lining up you would do 8! ...I'm not sure what to do if you can not have sally, mary, and Jan together. Thank you!

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Question 302034: From a deck of 52 cards, 5 cards are dealt and the order of the cards is not important. In how many ways can you receive at least one face card?
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Question 302061: Benito has 20 small balls of different colours: yellow, green, blue and black. 17 of the balls are not green, 5 are black, 12 are not yellow. How many blue balls does Benito have?
A) 3 B) 4 C) 5 D) 8 E) 15

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Question 302632: How many ways can 10 people be placed in alphabetical order according to their first names? Show how you know.
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Question 302632: How many ways can 10 people be placed in alphabetical order according to their first names? Show how you know.
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Question 302720: How to find how many 3-digit numbers can be made from the digits 2.4.6?
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Question 303199: how many different ways can 9 people be seated around a circular table?
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Question 303837: How many different ways can you score an 80 on a 10 question true- false quiz?
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Question 304036: What is the permutation of 20!
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Question 304324: A license plate number consists of three letters followed by three digits. How many different license numbers can be formed if repetition of letters and digits is allowed? How many different license numbers can be formed if repetition of letters and digits is not allowed?
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Question 304489: There are 8 true or false questions on a quiz. In how many different ways can they be answered? I got 2 to the 8 = 256
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Question 305213: A restaurant offers the following choices for breakfast:
Eggs: scrambled, fried, or poached
Meat: bacon, sausage, or ham
Toast: wheat, white, rye, or pumpernickel

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Question 305211: A restaurant offers the following choices for breakfast:
Eggs: scrambled, fried, or poached
Meat: bacon, sausage, or ham
Toast: wheat, white, rye, or pumpernickel

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Question 305224: 16 tennis players playing for 8 weeks. They play 4 on a court each week. How do I figure out the different number combinations(if I call each player a number 1-16)so they play the most players? I know I can start with 1,2,3,4 on court 1, 5,6,7,8 on court 2 etc. for the first week, but where do I go from there?
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Question 305646: How many outcomes of the last four digits on a telephone number?
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Question 305645: How many outcomes of the last four digits on a telephone number?
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Question 305659: A lock has three dials with the digits 0-9. How many codes to open the lock are possible?
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Question 306167: If you have 5 different colored dice how many different possibilities are there?
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Question 306272: Evaluate 14!/1!13!

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Question 306272: Evaluate 14!/1!13!

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Question 306579: If three cards are dealt from a deck of 52, what is the probability that the first card is a heart and the next two are both diamonds?
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Question 306621: in how many ways can 2 co-chairs be selected from a club of 20 students?
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Question 306985: how many ways can you answer a 6 true or false question test?
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Question 307043: how many different ways can you pick a 3 person committee from a group of 10
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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