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

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Question 747303: how many ways can you arrange 6 students in the front row if there are 30 total students?
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Question 747596: Six students ran a race. How many ways can they finish 1st, 2nd, and 3rd?
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Question 747595: how many teams of three can you make from a class of 27?
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Question 747619: In how many ways can the word "TOPO" be arranged
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Question 747608: How many permutations of 4 different letters are there, chosen from the twenty six letters of the alphabet (repetition is not allowed)?


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Question 747755: The number of ways in which 8 sweats of different sizes can be distributed among 8 persons of different ages so that the largest sweat goes to the younger assuming that each one of them gets a sweat
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Question 747836: Five friends are waiting in a line. How many different ways can they arrange themselves in that line?

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Question 747960: There are 20 members in a club. Five people are selected to go to the state conference. In how many ways can the five members be selected?
Methods tried: 20P5= 5!/(20-5)!
Thank you for your help

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Question 747976: How many different combinations of clothes can you make if you have 2 pairs of pants, 4 shirts, and 3 jackets
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Question 748021: In how many ways can three student-council members be elected from five candidates?

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Question 748088: How many different three-letter codes can be formed out of the word PEPPER? Is that both a combination and permutation problem?
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Question 748167: There are seven finalists for two scholarships. Four of them are girls and three of them are boys. In how many ways can the scholarships be awarded to one boy and one girl?

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Question 748260: If there are 12 appetizers and 7 entrees, how many different Special Dinners are there?
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Question 748336: how many ways can you buy two software titles from a choice of 12 ?
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Question 748639: Seven flute players are listed in the program in random order. How many different ways can the names be listed
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Question 748640: 250C150
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Question 748705: Can you please help me figure out how to evaluate: (100!)(24!)/(97!)(25!)
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Question 748710: Can you please help me with this word problem?
Nikki has a collection of 32 CDs, 18 r&b, and 14 hip hop. As she is leaving for a trip, she randomly chooses 6 CDs to take with her. What is the probability that nikki selects 3 r&b and 3 hip hop cds? Answer has to be 4 decimal places!
Thank you so much!!

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Question 748712: Please help!
How many distinguishable permutations are there for the Hawaiian word aloha?

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Question 748711: Can you please help me with this question?
Two dice are rolled. What is the probability the sum of the two dice will be a prime number?

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Question 748781: there are 9 women and 7 men in our class. how many different 4 person committees are possible if we want an equal number of men and women on the committees?

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Question 748941: In what proportion should water & wine be mixed to reduce price of wine from Rs. 150 to Rs.120/litre ?
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Question 749043: What is the value of. 4P2
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Question 749128: Can someone help me with this problem: Putting together notes for final. MUT SHOW WORK. Bless your heart.
Find the number of combinations when 13 objects are taken 4 at a time.
AND
Evaluate: P(1,5)

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Question 749248: Six different books will be displayed in the library window. How many different arrangements are there?
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Question 749359: the number of ways of arranging 5 women and 4 men so that the row begin and end with women
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Question 749394: Q15 In how many ways can we distribute seven apple and six oranges among 4 children so that each children receive at least one apple?
Q16 From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
Q17 A committee of 7 consisting of a chairman, vice chairman, a secretary, and 4 other member is to be chosen from a class of 20 students. In how many ways can this committee be chosen?
Q18 Weave and Kline, a software development company, has received nine new user requirement regarding a new computer system. In how many ways can these new user requirements be directed to three of the company's software developers if each of the software developers has to handle three new user requirements?
Q19 A restaurant has 6 different desserts. Find the number of ways a customer can choose
a. 1 dessert
b. 2 of the desserts
Q20 Given a class of 12 girls and 10 boys
a. In how many ways can a committee of five consisting of 3 girls and 2 boys be chosen?
b. What are the possible committees of five can be chosen at random from the class, consists of three girls and two boys?
c. How many of the the possible committees of five have no boys? (i.e. consists only of girls)

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Question 749388: plz help me:
Directions for Q1 to 3:
In a famous short-time game named CROSS, each player
puts a mark (O OR x) one by one inside a 3x3 grid (9 slots).
Two players face the following situation in between the
game.
A player will put his mark in a line such that:
(a) it already contains two of his own marks (for winning)
(b) it already contains two of the opponents marks (for
saving the game)
It is known that player always gives priority to Winning
over saving.
1. What could be the mark of the person who started the
game?
A) X
B) O
C) X or O
D) Data insufficient
2. The player who wins the match uses which mark?
A) X
B) O
C) X or O
D) Data insufficient
3. Probability of A (with symbol O), winning the game
if both players freely mark anywhere?
A) 0.76
B) 1
C) 0.5
D) 0.33

Click here to see answer by lynnlo(4176) About Me 

Question 749386: Plz some1 help me to solve this problem:
An 8 litre cylinder contains a mixture of oxygen
and nitrogen, the volume of oxygen being 16% of
the total volume. A few litres of the mixture is
released and an equal amount of nitrogen is added.
Then the same amount of the mixture as before is
released and replaced by nitrogen for the second
time. As a result, the oxygen content becomes 9% of
the total volume. How many litres of mixture is
released each time?

Click here to see answer by lynnlo(4176) About Me 
Question 749386: Plz some1 help me to solve this problem:
An 8 litre cylinder contains a mixture of oxygen
and nitrogen, the volume of oxygen being 16% of
the total volume. A few litres of the mixture is
released and an equal amount of nitrogen is added.
Then the same amount of the mixture as before is
released and replaced by nitrogen for the second
time. As a result, the oxygen content becomes 9% of
the total volume. How many litres of mixture is
released each time?

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Question 749537: If there is 14 people in a spelling bee how many ways can there be first second or third?
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Question 749782: A library has 8 tables and 42 chairs. There are several small tables with 4 chairs each and some large tables with 6 chairs each. How many tables of each type are in the library?
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Question 750030: How many different committees of 3 people can be chosen to work on a special project from a group of 7 people?
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Question 750303: How many different arrangements are there of the letters of the word SITTING? How many of these arrangements start with a repeated letter?
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Question 750356: in how many ways can a committee of 4 people be chosen out of 8 people?
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Question 750507: 2. How many ways are there to arrange 10 students in two lines? (a line must have at least 1 student)I used nCr on a TI 84+ Calculator and got 28, but i have a feeling I am rather mistaken. How do I go about solving this?
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Question 750715: In how many ways can the word "HOSPITAL" be arranged?
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Question 750262: A telephone number consists of seven digits, the first three representing the exchange. How many different telephone numbers are possible within the 717 exchange?
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Question 751100: ten students will participate in a spelling contest. how many outcomes for first,second, and third place are possible?
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Question 751182: Simplify Manually.
102!/(93!8!)

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Question 751204: In how many ways can a president and a vise-president be randomly selected from a class of 28 students?
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Question 751226: You plan to offer two or three choices of pizza in each of three categories-size,crust,and topping. The more types of pizza the better but you're limited by kitchen space to a total of 18 types. I have tries figuring out this problem.. I just can't! Can you help
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Question 751345: There are 5 airplanes ready to depart. Runway A and runway D are available. How many ways can 2 planes be assigned to runways without using the same runway?
Could you please tell me the answer, and teach me which is N and which is R from the permutation formula, it is a permutation right? Thank you so much for taking the time to answer my question.

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Question 751375: You will randomly choose 4 digits from the set {1,2,3,4,5,6} without replacement & put them in the order they were chosen how many different 4 digit can be made?
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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