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

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Question 857032: There are 10 children in a music class: 6 girls and 4 boys. In how many ways can the music instructor choose 2 girls and 2 boys to perform in a recital?
Click here to see answer by ewatrrr(24785)

Question 857059: Determine the number of arrangements for the letters of the word REMEMBER.
Click here to see answer by stanbon(75887)

Question 857061: Two fair dice are tossed. What is the probability that the sum of the top two faces is between 4 and 9?
Click here to see answer by ewatrrr(24785)

Question 857044: One number is selected from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. What is the probability that the number selected is less than 8 or even?
Click here to see answer by ewatrrr(24785)

Question 857242: There are 6 books on a reading list. Students must read 3 of the books on the list. In how many ways can a student select 3 books?
Possible answers:
20
60
120
360
Click here to see answer by chndnbl(31)

Question 857308: The organizing group which consists of 1 chairman, 1 financial secretary and 8 working staff is formed. The chairman and the finance secretary are chosen from 6 teachers while the 8 working staffs are selected from 20 students.
how many different organizing groups can be formed?
If it is possible to have an organizing group with all the working staff being boy, what are the possible numbers of boys among the 20 students?
Click here to see answer by Theo(13342)

Question 857328: There are 12 face cards in a standard deck of 52 cards. How many ways can you arrange a standard deck of 52 cards such that the first card is a face card?
Click here to see answer by Fombitz(32388)

Question 857352: how many ways select a captain and a vice captain from 20 member football team.
Click here to see answer by stanbon(75887)

Question 857278: a student takes an exam containing 10 multiple choice questions. The probability of choosing a correct answer by knowledgeable guessing is 0.2 At least 6 correct answers are required to pass. If a student makes knowledgeable guesses, what is the probability that he will fail?
Click here to see answer by ewatrrr(24785)

Question 857375: A secret code consists of 2 digits, followed by 2 letters, followed by 1 of the following symbols: @, #, %, and &. Digits and letters cannot repeat. How many secret codes are possible?

Click here to see answer by ewatrrr(24785)

Question 857399: How many permutations are there in a 3-letter code which can use the letters from A to Z (inclusive)?

Click here to see answer by Fombitz(32388)

Question 857659: A menu offers 7 different salads and 5 different entrees. How many ways are there to choose 3 salads and 2 entrees?
Click here to see answer by ben720(159)

Question 856887: Show that (n+1)! -3(n!) + (n-1)! = (n-1)!(n-1)�
Click here to see answer by Edwin McCravy(20054)

Question 855773: In the word DISCRETE how many :
1. 8 letter word can be formed
2. 7 letter word can be formed
3. 6 letter word can be formed
4. 5 letter word can be formedz
Click here to see answer by Edwin McCravy(20054)

Question 858065: How many computer passwords that consist of 3 different digits can be formed from among the digits 0 to 9?
Click here to see answer by Alan3354(69443)

Question 857977: If v,w,x,y,z are non negative integers,each less than 11,then how many distinct combinations of v,w,x,y,z satisfy v(11^4)+w(11^3)+x(11^2)+y(11)+z=151001
Click here to see answer by Edwin McCravy(20054)

Question 857969: How many positive integers less than 6000 may be written down without using the digits 6,7,8,9 and 0?
Thank you so much

Click here to see answer by Edwin McCravy(20054)

Question 857791: A 12-member committee is going to choose a chairman, vice-chairman, and secretary.

In how many ways can these people be chosen?
Click here to see answer by ben720(159)

Question 857822: how many different arrangement of the letters in the word "ellipses" can be formed if the consonants must be together?
Click here to see answer by Edwin McCravy(20054)

Question 857270: The number of permutation from the letter A to G.so that neither the set BEG nor CAD appears is ?
Click here to see answer by Edwin McCravy(20054)

Question 857728: At a restaurant a table has 12 place settings. A family of 7 is going to sit at that table. How many ways can the family arrange themselves around the table at each place setting?
Thank You! I am studing for an exam..this is one of the many types that will be on The tesT.!
Click here to see answer by Edwin McCravy(20054)

Question 856885: Ten cards are numbered 1 to 10. Three different cards are selected at random from these cards. What is the probability that the sum of the numbers obtained is at most 9?
Click here to see answer by Edwin McCravy(20054)

Question 853556: From a deck of 52 playing cards, how many different ways can a hand of 5 cards contain four of a kind? (4 cards have the same number and the 5th card of some other number and order is important).
Click here to see answer by Edwin McCravy(20054)

Question 858332: Eight horses are running in a race. In how many ways can these horses be awarded win, show, or place (without ties)?
Click here to see answer by checkley79(3341)

Question 858366: how many times does 8 go into 1576

Click here to see answer by rvfer(117)

Question 858470: How many six-symbol computer passwords can be formed using the letters A to J and the digits 3 to 7?
Click here to see answer by solver91311(24713)

Question 858513: how many 3-digit numbers are made of 3 different even digits and are divisible by 5?
Click here to see answer by Edwin McCravy(20054)

Question 858584: How can 5000! (a large factorial) be found numerically?
Someone, call him Igor for this problem :) Anyway - wants to know how
many groups of 50 are there in 5000.
I started working this using nCr = n! / r!(n-r)!
nCr = 5000C50, and chose to settle for a ball-park (estimated figure) quote,
yet have no idea although the number C must lie between astronomical and ∞.
50! is solvable, but was wondering if 5000! can be partitioned or reduced
so a hand calculator could work it. Any shortcuts here would be appreciated!
Click here to see answer by KMST(5328)

Question 858607: To cancel an electronic alarm, a 4-digit number must be entered into a code box. What is the maximum number of tries you have to cancel the alarm if a number can be repeated and if a number cannot be repeated. Can you explain how you got to the answer and also how to work it out on the Texas Instruments TI-84 plus?
Click here to see answer by Edwin McCravy(20054)

Question 858479: Four couples have purchased tickets to the school play. Their seats are next to one another in a single row. If each couple sits side by side, how many arrangements are possible
Click here to see answer by Edwin McCravy(20054)

Question 858418: using numbers 0 through 9, how many 6 digit numbers are possible if a leading 0 is allowed?

Click here to see answer by Edwin McCravy(20054)

Question 857413: There are 8 black balls and 5 red balls in an urn. If 5 balls are drawn without replacement, what is the probability that exactly 1 black ball is drawn?
Click here to see answer by Edwin McCravy(20054)

Question 857412: There are 9 black balls and 6 red balls in an urn. if 3 balls are drawn without replacement, what is the probability that no more than 1 black ball is drawn?
Click here to see answer by Edwin McCravy(20054)

Question 856864: in how many ways can 4 prizes be distributed among 5 person when
(i) no person get more than 1.
(ii) a person may get any number of prizes.
(iii) a person get all the prizes.
Click here to see answer by Edwin McCravy(20054)

Question 859091: how many combinations are there in a four digit code from 1-9 and you can't use the same number twice
Click here to see answer by edjones(8007)

Question 859512: a family has seven children . if this family has exactly two boys, how many birth and gender orders are possible.
Click here to see answer by stanbon(75887)

Question 859521: have 120 teams. Given that team rankings (wins) is random, what is the expected probability of one team being ranked in the top 10?
Click here to see answer by Fombitz(32388)

Question 859654: Please help me solve this question. You can program some CD players to choose randomly in which order to play the tracks on a record.
a. How many different choices are there for a CD with 7 tracks?
b. Suppose you program the CD player to play 5 of the tracks, chosen randomly. In how many ways can the choice be made?
for a, I think the answer is 5040 but i am not sure. For b, I think the answer is 21 but I feel like the gap between the two numbers is too big.
Click here to see answer by DrBeeee(684)

Question 859714: In how many ways can 6 people be seated on a sofa if there are 3 seats available ?
Click here to see answer by solver91311(24713)

Question 859713: In how many ways can a committee of 4 people be chosen out of 8 people ?
Click here to see answer by jim_thompson5910(35256)

Question 859043: relation of ncr,ncr-1,ncr+1

Click here to see answer by tommyt3rd(5050)

Question 859813: There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. If the selection is random, what is the probability of selecting a team of 4 girls and 6 boys?
Click here to see answer by ewatrrr(24785)

Question 859739: A student is to answer 11 out of 20 questions on a test. Find the number of ways the student can choose if the student must answer the first 6 questions on a test.
I'm thinking it might be (20p6)(14p5)?
P.S. I tried looking this up by reviewing past post but there were so many repeat questions that I gave up, sorry.
Click here to see answer by ewatrrr(24785)

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