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

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Question 878103: a restaurant offers a dinner special that has 12 choices for entrees 10 choices for side dishes and six choices for dessert. For the special you can choose one entree two side dishes and one dessert. how many different meals are possible
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Question 877952: an internet site requires a 8 character passwords, made up of 4 digits and 4 letters. it's required that the first number of the password be the number 9, without repetition of number or letters, how many different password can be made?
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Question 878355: find the number of permitations using all leters of the word management
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Question 878603: 7 things taken 2 @ a time. How many possible combos?
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Question 878594: An eight-character password is selected by choosing four lettere (case insignificant) and four digits
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Question 878580: A group of 5 entertainers will be selected from a group of 20 entertainers that includes "Small" and "Trout". In how many ways could the group of five include at least one of the entertainers "Small" and "Trout" ? I have tried setting it up as a combination and I just don't seem to be anywhere close to getting the correct answer. Please be specific in how to set up this problem for solving as I need to see the process in order to completely understand it for my final. THANK YOU
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Question 878670: in how many ways 5 physics,3 chemistry,3 maths books be arranged keeping book of same subject together
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Question 878677: six pennants are to be hung on a flagpole. in how many different orders can they be hung?
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Question 878793: my daughter forgot her pin to her cell phone, she swears the numbers were the upper four of the keypad, 2,3,5,6. we are not sure in which combination though. Can you tell me how many combinations of these numbers there are? my guess was because there' four numbers, it would be something like 4x3x2x1=24 combinations of the numbers? is this correct? any way to generate a list of the possible numbers to begin our input attempts? Thanks so much, Greg Powell
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Question 878823: Orick and Junia want to have three children. If there is a 50% chance of having a boy and 50% chance of having a girl. find the probability of having 2 boys and 1 girl (order is not important)?

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Question 878941: Last semester, a certain professor gave 31 As out of 318 grades. If one of the professor's students from last semester were selected randomly, what is the probability that student received an A?
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Question 878942: An oil-drilling company knows that it costs $25,000 to sink a test well. If oil is hit, the income for the drilling company will be $465,000. If only natural gas is hit, the income will be $150,000. If nothing is hit, there will be no income. If the probability of hitting oil is 1/40 and if the probability of hitting gas is 1/20, what is the expectation for the drilling company?
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Question 878944: Find the requested probability.
P(A) if P(A) = 0.3

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Question 878949: Two fair coins are tossed. What is the probability that at least one is a tail? (Enter the probability as a fraction.)

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Question 878950: A single card is drawn from a standard deck of cards. Find the probability if the given information is known about the chosen card. A face card is a jack, queen, or king.
P(face card|queen)

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Question 878952: A state's license plates consist of three letters followed by four numerals, and 248 letter arrangements are not allowed. How many plates can the state issue?
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Question 878957: A state's license plates consist of three letters followed by four numerals, and 248 letter arrangements are not allowed. How many plates can the state issue?
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Question 878959: If a nine or an eleven occurs on the first roll, the player wins. What is the probability of winning on the first roll?
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Question 879135: How many distinguishable ways can be written using all the letters in the word ALGEBRA?
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Question 879154: Question 9. 9. Mr. Davis has 15 students in his class. He wants to send 3 of his students to pick up books for the class. How many combinations of students can he choose?

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Question 879149: There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. What is the probability that a randomly chosen team has 3 or 4 girls
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Question 879169: if there is 4 different types of meat and 5 different types of vegetable. and a meal consists of 1 meat and 2 vegetables. how many different types of meals can you get.
thanks

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Question 879172: A class consists of 30 students of whom 20 are female students. Determine the number of committees of 5 that can be formed if each consists of exactly 3 female students.
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Question 879192: Of 25 members of a senior honors engineering society, 18 are men and 7 are women. The adviser chooses 4 of them to be on the executive committee. What is the probability that exactly 2 of the members of that committee will be women, if every student is just as likely to be chosen?
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Question 879206: There are 15 students in a lab. Count the total number of ways that 4 can receive A's and 7 receive B's.
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Question 879235: If you have 9 people and they each selected a song, created a list of 9 songs and those 9 individuals had to guess using a random number generator who selected each song on the list. On average how many would be get right? What is the formula?
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Question 879303: A student must answer four of the six essay questions on a history test. how many different selections are possible?
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Question 879345: You wish to form two-member committees (two people on a committee) from 4 couples. The only catch is that no couple is allowed to serve together with their spouse on a committee. How many possible committees can be formed?
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Question 879435: How many 4 digit numbers can you make using the numbers 1 - 5 with no repetitions?
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Question 879434: Suppose 2 events A and B are mutually exclusive and that Pr[A] = 0.3 and Pr[B] = 0.5. What are the probabilities that (a)either events occur, (b) A occurs and B does not, and (c)both A and B occur?
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Question 879463: Sixty-two percent of college students have laptop computers, and sixty-eight percent have MP3 players. If 20% of college students own neither of these types of electronics, what is the probability that a student selected at random will own both of the two devices?
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Question 879495: Thank you so much for helping me!!
Here is the problem: I have three stacks of 38 cards with words on them. Pile #1 (38cards), Pile #2 (38cards), and pile#3 (38cards). How many 3 word combinations can I make with the cards using one card from each stack. The stacks will stay in the order 1,2, 3. .

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Question 879528: Thanks for taking the time to answer my question. I think it uses combinations and is a bit tricky:
The possibility that a basketball player will make a given free throw is 3/5. To find the probability that the player makes exactly 9 out of his next 10 free throws, evaluate the term 10 C 9 (3/5)^9(2/5)^1 in the expansion of (3/5 + 2/5)^10
Thank you, please include the answer as well as the steps how you got that answer (so I can understand the problem). -Leo

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Question 879553: y=2x^2+12x+20

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Question 879608: Thanks In Advance :)
A club wants to choose a committee of 4 people from its 12 members.

How many ways can the committee be chosen?

A.
48

B.
11,880

C.
19,958,400

D.
495 (I think it's this one)

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Question 879795: If the number of 5 digit combinations that can be made from the numbers 1 through 75 (where the order doesn't matter) is: 17,259,390 Using the formula: ( (75x74x73x72x71) [2,071,126,800] / (5x4x3x2x1) [120] ), then why does the VA Lottery state that your chances of getting all 5 numbers are 18,492,204 to 1?
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Question 879929: From a batch of 3000 light bulbs, 100 were selected at random and tested. If 5 of the light bulbs in the sample were found to be defective,how many defective light bulbs would be expected in the entire batch?
A. 15
B. 60
C. 150
D. 300
E. 600

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Question 879939: using alphabet cards what is the possibility of drawing a M
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Question 879972: Consider a bench on which six student can sit .In how many ways can 3 girls and 3 boys sit on the bench if no girls sit next to one another and also no boys sit next to one another?it is related with permutation and combination
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Question 879874: How many five-letter "words" can be made from the letters A,B,C,D,E,F,G,H,I,J if repletion (a)is allowed or (b) is not allowed?
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Question 879880: Adam is looking in the freezer. He finds 4microwave dinners an 3different veggies. How many combinations of one dinner and one veggie are there?
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Question 880095: how many groups of four can you get out of six people
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Question 880246: A security system uses a 6-letter password, but no letter can be used more than once. How many possible passwords are there if 18 of the letters of the alphabet can be used by the system? I am using the formula: Permutation w/ N= 18 and r = 6. Is that correct?
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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