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

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Question 541910: How many ways can
20 diseases be selected from 30?
Click here to see answer by stanbon(75887)

Question 542341: How many different vertical arrangements are there of 7 flags if 4 are white, 2 are blue, and 1 is red?
Click here to see answer by stanbon(75887)

Question 543385: In how many different ways can you answer a multiple choice test that has 9 questions and 3 choices for each answer?
Click here to see answer by stanbon(75887)

Question 544419: in a group of 25 students, 14 play tennis, 16 play gold, and 3 students play neither. what is the probability that a given student plays both tennis and golf?
Click here to see answer by Edwin McCravy(20054)

Question 544519: How many 7-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 if the first digit cannot be 0? Repeated digits are allowed.
Click here to see answer by hitarth(1)

Question 544179: There are twenty women and fifteen men at a party. In how many distinct ways can you form ten couples consisting of one man and one woman?
***
I thought it would be 15C10 * 20C10 * 10! - you choose the men and the women; then the first woman has ten choices, the second has nine, etc. However, I'm not sure what really distinguishes this from a basic Fundamental Counting Theorem problem once you have chosen the men and women; under that interpretation, the 10! is unnecessary.
Thank you!
Click here to see answer by sudhanshu_kmr(1152)

Question 544804: how many permutations are in the number 2713?
I am looking for all choices
thanks!
Click here to see answer by stanbon(75887)

Question 544792: The Ratio from males to females in math 092 class is 2:3
How many males are there in a class with 24 females
Click here to see answer by rfer(16322)

Question 544764: A ship carries four signal flags, each a different color. The order in which the flags are hoisted on the flag pole constitutes a signal.
a) How many different signals can be made when all four flags are raised?
b) How many different signals can be made using three flags?
c) How many different signals can be made in total using any number of the four flags?
Click here to see answer by sudhanshu_kmr(1152)

Question 545122: There are 7 performers who are to present their acts at a variety show. How many different ways could their performances be scheduled?
Click here to see answer by jim_thompson5910(35256)

Question 546427: We need to create three digit code numbers that must begin with a 7. How many such codes can be made?
A) 107
B) 27
C) 700
D 100

Click here to see answer by Alan3354(69443)

Question 547217: The internal telephone numbers in the phone system on a campus consist of five digits with the first digit not equal to zero. How many different numbers can be assigned in this system?

i would believe that it would be 9 * 10 * 10 * 10 * 10. but i am not quite sure.
would this question be labeled as combination or permutation?
Click here to see answer by mathie123(224)

Question 547523: In a group of 7 students, how many different ways can five different books be given to them(one person can recieve as many as 5 books)?
Click here to see answer by nyc_function(2741)

Question 547612: An ice scream store sells 27 flavors of ice cream how many 3 dip sundaes are possible if order is not considered and no flavor is repeated?

Click here to see answer by edjones(8007)

Question 547607: A club with seven members is to choose three officers, if each office is to be held by one person and no person can hold more than one office in how many ways can those offices be filled?
Click here to see answer by edjones(8007)

Question 547666: how many 4 digit even numbers can be formed if repeats of digits are not allowed
Click here to see answer by mathie123(224)

Question 547666: how many 4 digit even numbers can be formed if repeats of digits are not allowed
Click here to see answer by andy_mitc(1)

Question 547741: An experiment consists of flipping two coins and noting the face of each coin as
Heads or Tails.
a)What is the sample space for this experiment?
b. What is the probability of getting exactly two heads?
c. What is the probability of getting at least one head.

Click here to see answer by mathie123(224)

Question 548137: Find the number of ways 7 students can be arranged in a row?

Click here to see answer by jim_thompson5910(35256)

Question 548199: total number of ways in which six 't' and four '-' signs can be arranged in a line such that no two '-' signs occur together is ?
Click here to see answer by Edwin McCravy(20054)

Question 548301: In how many different ways can teams of 2 tennis players be selected from a group of 5
players?
Click here to see answer by stanbon(75887)

Question 548339: 9 people are sitting a round a table. How many ways can they sit?
Click here to see answer by stanbon(75887)

Question 548357: How many arrangements can be formed of the letters EXAMINATION so that vowels occupy odd places.
Click here to see answer by Edwin McCravy(20054)

Question 548371: HOW MANY DIFFERENT WORDS (REAL OR NON-REAL) CAN BE FORMED FROM THE LETTERS OF THE WORD MAKEUP?
***MY ANSWER WAS 720**
Click here to see answer by Edwin McCravy(20054)

Question 548056: in how many ways can nine students be seated in a row containing nine desks if two students must not be seated next to each other? my thinking is 9!2! because u have 9 students but 2 of them have a stipulation ...
Click here to see answer by scott8148(6628)

Question 548396: The four numbers a < b < c < d can be paired in six different ways. if each pair has a different sum, and if the four smallest sums are 1,2,3 and 4, what are all possible values of d
Click here to see answer by Edwin McCravy(20054)

Question 548886: A gym teacher has 7 sixth grade students who would like to play on the school's hockey team. In how many ways can these athletes be grouped to make up a hockey team? [Make a list]
Click here to see answer by Alan3354(69443)

Question 548939: How many ways can a 3-people committee be chosen from 10 twins(20 people)? Restriction: No twins can both exist in this committee. (e.g Assume A & B are twins, if A is in the committee, B cannot be in.)
Click here to see answer by josmiceli(19441)

Question 548949: A group of��7 education majors, 12 art majors, 5 sociology majors, 8 math majors, and 3 engineering majors must select a
committee of five.��How many committees are possible if the committee must contain:
d. at most 2 sociology majors
I understand the 5C2 + 5C1 part but not sure how to put it together with the other groups
Click here to see answer by stanbon(75887)

Question 548883: How many different license plates are possible if a state uses two letters followed by a four-digit integer (leading zeros are permissible and the letters and digits can be repeated)?
Click here to see answer by mathie123(224)

Question 548974: A true-false test contains 8 questions. In how many different ways can the 8-question test be answered?
Click here to see answer by mathie123(224)

Question 548992: how many possible ways can a student answer 10 multiple choice questions where each question has 4 options
Click here to see answer by mathie123(224)

Question 549246: In how many ways can the following prizes be given away to a class of 20 boys : first and second Classical, first and second Mathematical, first Science and first French ?
Click here to see answer by mathie123(224)

Question 549247: In how many ways is it possible to draw a sum of money from a bag containing a sovereign, a half-sovereign, a crown, a florin, a shilling, a penny, and a farthing ?
Click here to see answer by solver91311(24713)

Question 549367: How many 6-letter "words" are possible using the letters A, B, C, D, E, F (no repeats allowed)?
Click here to see answer by Alan3354(69443)

Question 549248: From 3 cocoa nuts, 4 apples, and 2 oranges, how many selections of fruit can be made, taking at least one of each kind ?
Click here to see answer by stanbon(75887)

Question 549761: how many possible ways to seat 15 kids in 15 seats?
out of 15 students how many ways to choose 5 out of the 15 students for a project?
Click here to see answer by mathie123(224)

Question 549805: In a shipment of 100 laptops, 6 are defective. If a person buys two laptops from that shipment, what is the probability that they are defective?
Click here to see answer by stanbon(75887)

Question 549852: P(7,3) = ?
Click here to see answer by jim_thompson5910(35256)

Question 549852: P(7,3) = ?
Click here to see answer by stanbon(75887)

Question 549939: There are 2 work each of 3 volumes and 2 work each of 2 volumes. In how many ways can the 10 books be placed on a shelf so that the volumes of same work are not separated ?
Answer- 3456
Click here to see answer by Theo(13342)

Question 549966: How many numbers divisible by 5 and lying between 5000 and 9000 can be formed from the digits 5, 6, 7, 8 and 9?
Click here to see answer by TutorDelphia(193)

Question 549700: Directions: Form a group of 2 to 4 people. Select someone to record the group�s responses for
this activity. All members of the group should work cooperatively to answer the questions. If
your instructor asks for the results, each member of the group should be prepared to respond.
Minimum Wage The table shows the minimum wage for
three different years.
(a) Make a scatterplot of the data in the viewing rectangle
[1930, 2010, 10] by [0, 6, 1].
(b) Find a quadratic function given by
that models the data.
(c) Estimate the minimum wage in 1976 and compare
it to the actual value of $2.30.
(d) Estimate when the minimum wage was $1.00.
(e) If current trends continue, predict the minimum
wage in 2009. Compare it to the projected value of
$7.25.
Click here to see answer by richard1234(7193)

Question 550045: If there are four red, five green and six yellow apples, how many selections of nine apples are possible if three red apples, three green apples and three yellow apples are to be selected?
Click here to see answer by stanbon(75887)

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