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

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Question 866926: There were 20 girls and 30 boys in the second session. What is the percentage of boys in the second session of swimming lessons?
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Question 867006: Using the Binomial Theorem and Pascal's Trinagle write out the binomial expression for (5k+4) to the 7th power.
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Question 867162: Three fair quarters and an unfair quarter with two heads are placed in a bag. One quarter is selected, and tossed. What is the probability of getting heads?
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Question 867204: What is the probability that a couple will have at least three sons if they plan to have 4 children and if the probability of having a son equals the probability of having a daughter?

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Question 867201: Which factorial would give the amount of different combinations that can be made from two letters and three digits (0-9)?
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Question 867219: A college planning committee consists of 3 freshman, 4 sophomores, 5 juniors, and 2 seniors. A subcommittee of 4 consisting of 1 person from each class is to be chosen. How many different subcommittees are possible?
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Question 867220: Find out in how many ways the operation can be performed? (Permutation & Combination)?
i) In how many ways can a committee of 5 or more be formed from 12 persons?
ii) In how many ways can a committee of 5 be formed from 12 persons if only two of a group of 3 persons must always be included?
All I know is it must be combination cause order/arrangement does not matter.
I know to solve by formula too; but confused how to begin. Help...

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Question 867228: A class in probability theory consists of 6 men and 4 women. An examination is given, and the students are ranked according to their performance. Assume that now two students obtain the same score. a) How many different rankings are possible? b) If the men are ranked just among themselves and the women are ranked just among themselves, how many different rankings are possible?
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Question 867225: A class in a probability theory class consists of 6 men and 4 women. An examination is given, and the students are ranked according to their performance. Assume that no two students obtain the same score. A) How many different rankings are possible? B) If the men are ranked just among themselves and the women just among themselves, how many different rankings are possible?
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Question 867295: A state's license plates consist of three letters followed by three numerals, and 249 letter arrangements are not allowed. How many plates can the state issue?
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Question 867304: Decide whether you would use a permutation, a combination, or neither. Next, write the solution using permutation notation or combination notation, if possible, and, finally, answer the question.
Tom is leading a workshop for 16 people. He wants each person to meet every other person (shake hands once). How many handshakes occur?

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Question 867360: A task force studying sex discrimination wishes to establish a subcommittee. If the subcommittee is to consist of 11 members chosen at random from a group of 15 men and 18 women, find the probability that the subcommittee consists of the following?
(a) 8 men and 3 women (Round your answer to two decimal places.)

(b) all women (Round your answer to seven decimal places.)

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Question 867481: Given a group of students: G=(Allen,Brenda,Chad,Dorothy,Eric) or G=(A,B,C,D,E)count the different ways of choosing the following officers or representatives for student congress. Assume that no one can hold more than one office.
A president, a secretary, and a treasurer, if the president must be a woman and the other two must be men

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Question 867569: A task force studying sex discrimination wishes to establish a subcommittee. If the subcommittee is to consist of 11 members chosen at random from a group of 19 men and 19 women, find the probability that the subcommittee consists of the following?
(a) 6 men and 5 women (Round your answer to two decimal places.)
(b) all women (Round your answer to seven decimal places.)

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Question 867569: A task force studying sex discrimination wishes to establish a subcommittee. If the subcommittee is to consist of 11 members chosen at random from a group of 19 men and 19 women, find the probability that the subcommittee consists of the following?
(a) 6 men and 5 women (Round your answer to two decimal places.)
(b) all women (Round your answer to seven decimal places.)

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Question 868066: A code consists of 2 letters and then 4 digits. Any of the letters and numbers can be repeated. How many different codes are there?
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Question 868207: A dish contains 8 different candies. How many different of 3 candies can be made?
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Question 868232: The bank asks you to create a 4 digit PIN Number for your ATM card. How many different combinations can you make using the digits 0-9 without repeating a digit?
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Question 868305: how may different four digit numbers can you make using 1,2,3,4,5,6,7,8,9 if no digit appears more than once in a number
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Question 868303: A single die is rolled twice and the results on each role is recorded.
Let event F= (the sum of the faces is 9)
Find P(F)

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Question 868313: The scale of the map is 3/4 inch=11 miles. How many miles is 5.25 inches on the map?
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Question 868318: How many different four-letter radio station call letters can be formed if the first letter must be K or W?
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Question 868337: 9 students are competing in a spelling bee. in how many orders can they finish? In how many ways can they finish 1st-4th
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Question 868324: How many 3-digit numbers greater than 300 are there that have different digits?

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Question 868363: One card is dealt from a standard 52-card deck of cards .find each of the probabilities below:
A.) let event E= {the card drawn is a club }
Find P(E)
B.) let event F= {the card drawn is a red card that is greater than four and less than 9}
Find P(F)

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Question 868376: Use the given information to find the indicated probabilities. P
A) P(A)=.7, P(B)=.9, P(A U B)=1.2
Find P (A Or B)
B) A and B are mutually exclusive. P (A U B)=1.5, P(B) =.7
i) Find P(A)
ii) Find P(A')

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Question 868419: An electronics store receives a shipment of 30 graphing calculators, including 7 that are defective. 4 of the calculators are selected to be sent to a local high school. How many selections can be made using the original shipment?
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Question 868117: 900!/(50!-5!)
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Question 868553: In a class of 40 students, 14 of which are girls, 6 students are to be selected at random.
a. In how many ways can their teacher choose 6 students?
b. In how many ways can their teacher form a committee consisting of 3 girls and 3 boys?
c. In how many ways can their teacher form a committee consisting of 2 girls?
d. What is the probability that at least two girls are chosen?

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Question 868459: how many three digit number can be formed using all the available digits (0-9) such that number starts with an odd number and ends with even number if repetition is allowed.

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Question 868710: a teacher put five people lettered A,B,C,D and E in a line-up, standing in spots numbered one through six from left to right. there is one empty space. Person E is the third person from the left. Person A is to person B's immediate left. If person D stands in space six swith no one beside him, where is person C
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Question 868710: a teacher put five people lettered A,B,C,D and E in a line-up, standing in spots numbered one through six from left to right. there is one empty space. Person E is the third person from the left. Person A is to person B's immediate left. If person D stands in space six swith no one beside him, where is person C
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Question 868916: A committee of 4 people is to be chosen from 5 married couples. find in how many ways the committee can be chosen if the committee should include at least one woman.
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Question 868067: I am having trouble with the following questions, coult you help me?
If a building has six door to the outside how many different ways can you enter and leave? Also how many ways can you enter and leave by a different door?
Thank you in advance

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Question 869042: What are all of the 720 arrangements of the numbers 1, 2, 3, 4, 5, and 6?
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Question 869109: The following sets represent the numbers that can be used on little league jerseys.
A={4, 5, 8, 9}
B={0, 1, 3, 6, 9 }
C={1, 2, 4, 7, 8}
D={2, 3, 5, 9}
How many elements are in the set (A∪B) ∩ (C∪D)?

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Question 869249: Determine the set of points where f (x) ≥ g (x), if f (x) = x2 – 4x and g (x) = x – 6. You may solve this either algebraically or graphically by graphing calculator.
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Question 869564: Solve 2x^2 -7x=15 by factoring.
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Question 869583: Given the equation -5(x-2)^2-1=y
a. Identify the vertex.
b. Identify the axis of the symmetry.
c. Identify the direction of the graph (whether it opens up or down).

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Question 869581: Solve 5x^2-13x+6=0 by a graph or a table. Show the part of the table that applies. Give three values at each point of the solution. Label the solution on the graph.

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Question 869601: You have 180 yards of fencing to use on three sides of a garden. The fourth side is the tool shed.
a. What is the maximum area that you can fence?
b. What are the dimensions of the garden?

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Question 869717: What are all of the 720 arrangements you can put the numbers 1, 2, 3, 4, 5, and 6. I know that is 6!. But I would like to know all of the arrangements.

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Question 869788: in a row of girls, a girl is 7 th from left end and 14 from right end.how many girls are there in row
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Question 869800: the local hobby store has 17 model airplanes to display. If the front case holds 6 models, how many ways can 6 planes be chosen for the front of the store
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Question 869603: In testing the effects of a drug, the percentage of the drug in the blood stream was given by p = 0.090t – 0.015t^2, where t is the time (in hours) after the drug was administered.
a. What is the maximum number of hours that the drug is in blood?
b. How much of the drug is in the system after 15 minutes?
c. How long is at least 12 percent of the drug in the system?

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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