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

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Question 1019557: Prove that nCr=nC(n-r).
Click here to see answer by Alan3354(69443)

Question 1019557: Prove that nCr=nC(n-r).
Click here to see answer by mathmate(429)

Question 1019559: If there are 12 persons in a party and each of them shake hands with all others.What is the total number of shake ?
Click here to see answer by ikleyn(52776)

Question 1019807: How many different 4-digit numbers can be formed from the digits 1,3,5,6,8, and 9 if no repetition of digits is allowed?

Click here to see answer by Edwin McCravy(20054)

Question 1019783: There are 5 students in a small class. To make a team, the names of 3
of them will be drawn from a hat. How many different teams of 3 students are possible?
Click here to see answer by Edwin McCravy(20054)

Question 1019564: A team plays 15 games a season. How many ways are there to
end up with 6 wins and 9 losses for the season.
Click here to see answer by Edwin McCravy(20054)

Question 1019477: This quarter, a survey of 110 students at De Anza College
finds that 60 take math, 50 take English, and 40 take
history. Of these 25 take English and math, 20 take English
and history, 20 take math and history, and 15 take all three
subjects. Draw a Venn diagram and determine the following.
a. The number of students taking math but not the other
two subjects.
b. The number of students taking English or math but not
history.
c. The number of students taking none of these subjects.

Click here to see answer by Edwin McCravy(20054)

Question 1019947: in a certain general assembly three major prizes are at stake.In how many ways can the first second and third prizes be drawn from a box.containing 120 names?

Click here to see answer by mathmate(429)

Question 1020037: An insurance company has 1000 polies of men of age 50. the company's estimate that the probability that a man of 50 dies within a year is 0.02. what is the expected number of claims that the company can expect from its beneficiaries of these men within a year

Click here to see answer by solver91311(24713)

Question 1020101: A box contains 7 white balls and 6 red balls. If Van chooses 9 balls at random from the box, what is the probability that he will select 4 white balls and 5 red balls?
I had tried 7/9 X 6/8 , 4/7 X 5/6. Also tried (7/9)^2 X (6/8)^2....the answer is supposed to be .294, but I can't get that. Thanks
Click here to see answer by richard1234(7193)

Question 1020224: A baker makes digestive biscuit whose masses are normally distributed with a mean of 26g and a standard deviation of 1.9g. The biscuits are packed by hand into packets of 25. Assuming the biscuits are a random sample from the population, what is the distribution of the total mass of biscuits in a packet and what is the probability that it lies between 598 and 606.
Click here to see answer by robertb(5830)

Question 1020223: A manufacturer makes two models of an item:modelI,which accounts for 80% of unit sales,and modelI I,which accounts for 20% of unit sales.Because of defects,the manufacturer has to replace (or exchange) 10% of its modelI and 18% of its modelI I.If a model is selected at random,find the probability that it will be defective.
Click here to see answer by robertb(5830)

Question 1020210: A garden has 15 slots for flowering pots. In how many ways can the pots be arranged if the garden is circular?
Click here to see answer by mathmate(429)

Question 1020261: Consider the following game that involves tossing a die. If the outcome is an even number,you win SZL20. If the outcome is 1 or 3,you lose SZL10. If the outcome is 5,you lose SZL30.What are the expected winnings?
Click here to see answer by Fombitz(32388)

Question 1020300: I have a 4-digit pin. Numbers allowed for each digit are 0 thru 9. The numbers do not have to be used only once, but can be used up to 4 times. (Ex.: 1111, 1010, etc.).
How many possible combinations/permutations exist for this 4-digit code, or a 6-digit code? Could you please include the formula used to obtain the answer?
Thank you,
David
Click here to see answer by Fombitz(32388)

Question 1020410: 1.A very small library has only 4 books that you can borrow.the library allows you to borrow 1,2,3 or 4 books at a time.assuming tha you borrow at least one book ,how many different selections can you make?
2. Lisa makek up a series of numbers.he finds each number in the series by multiplying the previous number by 3 & adding 5.if his fifth number is 767, what must his first number have been?
Please help me
Click here to see answer by ikleyn(52776)

Question 1020505: A password must contain 4 digits from 0-9 and the digits must not be repeated. How many combinations are possible?
Is the answer 10X9X7X8= 5040?
What if its a 4 digit number? Then will we have the answer as: 9X9X8X7?
Thanks
Ekta

Click here to see answer by Fombitz(32388)

Question 1019181: Find the number of arrangements of 4 letters from the word MATHEMATICS.
Click here to see answer by Edwin McCravy(20054)

Question 1018796: In a box there are: 7 red books, 5 white books, and 6 blue books. Three books are selected.
How many different ways can this be done if the selection:
(a) must contain one of each color? c(7,1)c(5,1)c(6,1)= 210
(b) must contain all the same color? c(7,3)+c(5,3)+c(6,3)=65
(c) must include more than one color? I'm not sure how to set this up can you please guide me through?
Click here to see answer by Edwin McCravy(20054)

Question 1020661: 7p3/3!
Click here to see answer by Fombitz(32388)

Question 1020714: In how many ways can you divide eight people into four groups of two?
Click here to see answer by stanbon(75887)

Question 1020647: Two bowlers....what are the odds of getting the same exact number pins with each throw through five frames?
Player 1. 1(8,0) 2(7,3...spare) 3(10...strike)
Player 2. 1(8,0) 2(7,3...spare) 3(10...strike)
Same number of pins each time thru 5(FIVE!!!!) frames!
This happened to a friend and I last night while bowling.
Yes, I did think to take a picture.
Click here to see answer by richard1234(7193)

Question 1020937: A student appear a test of 5 subjects.how many different ways he can be failed
Click here to see answer by mathmate(429)

Question 1021029: (n-1)(n sqaured + n)
Click here to see answer by Alan3354(69443)

Question 1020987: If no digit is repeated in any number, how many four-digit numbers can be formed out of the digits 1, 2, 3, 4, 5, 6, 7? How many of these numbers will exceed 4000?
Click here to see answer by mathmate(429)

Question 1021131: in how man different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?
a.2880
b.1400
c.1200
d.3212

Click here to see answer by robertb(5830)

Question 1021255: Out of 6 PDP and 5 ACP party members, four are to be selected. In how many ways can this be done so as to include
Click here to see answer by macston(5194)

Question 1021307: Carl is choosing a four-character password for his cell phone. The password can contain letters and digits only, and can't include repeating characters. How many passwords are possible?
Click here to see answer by Fombitz(32388)

Question 1021473: Two fair dice are rolled 5 times. Let the random variable x represent the number of times that the sum 11 occurs. The table below describes the probability distribution. Find the value of the missing probability.
x P(x)
0 0.75141884282545
1 0.221005542007485
2 0.0260006520008806
3 0.00152945011769886
4
5 5.29221494013446e-07
Click here to see answer by Fombitz(32388)

Question 1021258: In how many ways can 6 trees be planted in a circle?
Click here to see answer by FrankM(1040)

Question 1021686: The table below shows the grade-level distribution for the school basketball team.
freshman-2
sophomore-4
junior-8
senior-15
A local television station wants to interview 8 students from the team. How many different ways can exactly 4 seniors and 4 juniors be selected for the interview?
Click here to see answer by mathmate(429)

Question 1021719: You take the letters in the word HAPPY and write each one on a slip of paper. You then place the pieces of paper in a basket. If you pull out the pieces of paper one at a time without replacement, what is the probability that you will spell out the word HAPPY?
so i thought you'd solve for P(E)' for the letters are not in order then I just totally got lost. Please help!!
Click here to see answer by FrankM(1040)

Question 1021798: A license plate consists of two letters followed by four digits. How many licence plates are possible if repetition is not allowed? Note: The plate "MP 0123" is allowed
Click here to see answer by Edwin McCravy(20054)

Question 1021790: How many eight digit numbers are there in which appears 3
different digits where the largest digits appears twice
and the other two appears three times each. Assume 0
cannot be used at all.
Click here to see answer by Edwin McCravy(20054)

Question 1021265: How many ways can a basket schedule exhibition games with three teams if they are all available on any of 6 possible dates?
Click here to see answer by Edwin McCravy(20054)

Question 1021261: Ten people are going on a skin-diving trip in 3 cars that will hold 2, 4 and 5 passengers respectively. How many ways is it possible to transport 10 people to the skin lodge?
Click here to see answer by Edwin McCravy(20054)

Question 1021867: I have total 3 things and 5 slots . How can i fill this 5 empty slots using only 3 things ? please answer me . thanks in advance
Click here to see answer by mathmate(429)

Question 1021854: How many 8 digit numbers are there with 3 different digits,
one appearing twice and the other two appearing 3 times each.
Assume zero cannot be used at all.
Click here to see answer by Edwin McCravy(20054)

Question 1021973: Thirty three students went out for junior high football.How many ways can the coach create a lineup of 11 players?

Click here to see answer by stanbon(75887)

Question 1021886: How many 8 digit numbers are there with 3 different digits, 1 appearing twice and the other two appearing three times each? Assume zero cannot be used at all.
Click here to see answer by Edwin McCravy(20054)

Question 1022040: The letter of the word of COCHIN are permuted and all the permutation are arranged in alphabetical order as in English dictionary.the numbers of word before the word COCHIN.
Click here to see answer by Timnewman(323)

Question 1022046: in how many ways letters of word "ARRANGEMENT" can be arranged so that 2 A's and 2 R's do not come together.

Click here to see answer by Edwin McCravy(20054)

Question 1021882: How many 6 digit numbers are there with 3 different digits each of them repeated, if the only digits permitted are members of the set {1,2,3,5,7,8,9,}.
Click here to see answer by richard1234(7193)

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