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

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Question 1116031: Hello, I was wondering if you would be able to help me with this question:
Four cards labeled A, B, C, and D are randomly placed in four boxes labeled A, B, C, and D. Each box receives exactly one card.
In how many ways can the cards be placed in the boxes?
I thought this would be 4 x 4, for 4 cards and 4 boxes. But the answer is 24. I don't understand where the extra numbers are coming from. Thanks!
Click here to see answer by rothauserc(4718)

Question 1116033: In a shipment of 22 smart phones, 3 are defective. How many ways can a quality control inspector randomly test 5 smart phones, of which 3 are defective?
I tried doing C(5,3) and P(5,3). Neither are correct. It says the answer is 171. I really don't know what I'm doing wrong. Thanks in advance.
Click here to see answer by stanbon(75887)

Question 1116159: What is the probability that a randomly chosen four-digit number contains no repeated digits?
Click here to see answer by ikleyn(52776)

Question 1116160: Each of 9 different books is to be given at random to Rebecca, Sheila, or Tom. What is the probability that Rebecca receives 2 books, Sheila receives 4, and Tom receives 3?
Click here to see answer by ikleyn(52776)

Question 1116072: Ten students are to sit for an examination. Four students are doing mathematics and the other 6 different subjects. In how many ways can they be seated in a row if students doing mathematics are not to sit together?
The solution for this is 6!x7x6x5x4 but I got taught a different method and it did not work. I was taught to group all the maths people together so that there are now 7 groups. I then did 10!-7! to get the number of ways maths people not sitting together. I am really struggling with this questions and I would really appreciate it if you could post the solution and explain how you got to the answer (which is 604800). Thank you!
Click here to see answer by KMST(5328)

Question 1116300: How many subsets of {m,a,t,h,r,o,c,k,s} contain exactly 5 elements?
Click here to see answer by ikleyn(52776)

Question 1116297: In the men's 5000m race at the 2008 Olympics, there were 15 runners in the final. How many different ways could the gold, silver, and bronze medal be given out?
Click here to see answer by ikleyn(52776)

Question 1116296: Suppose that there are 10 people at the head table for a banquet. Each time a toast is given the 10 people raise their glasses in a toast and every person pings glasses exactly once with everyone else. If four people give toasts before the meal, how many pings will there be at the head table?
Click here to see answer by ikleyn(52776)

Question 1116305: A committee of 4 is to be chosen at random from among 5 women and
6 men. What is the probability that the committee contains at least
3 women?
Click here to see answer by Edwin McCravy(20054)

Question 1116304: A license plate consists of 2 letters followed by 4 digits followed by 1 letter.
How many license plates are possible if no letter is repeated and no digit is repeated? I have 26*25*10*9*8*7*24.
How many such license plates are possible of letters may be repeated, digits may be repeated, but the last letter must be Z? I have 26*26*10*10*10*10*1.
Click here to see answer by Edwin McCravy(20054)

Question 1116313: There are 4 freshman, 6 sophomores, 7 juniors, and 3 seniors on a school field trip. If three students are randomly selected to carry water bottle cases, what is the probability that they are all juniors?
Would it be 7/13?
Click here to see answer by ikleyn(52776)

Question 1116314: Suppose a fair coin is flipped 12 times. What is the probability that it will land heads exactly one time?
Click here to see answer by ikleyn(52776)

Question 1116315: Suppose a fair coin is flipped 12 times. What is the probibility that it will land heads at least one time?
Click here to see answer by ikleyn(52776)

Question 1116311: There are 4 freshman, 6 sophomores, 7 juniors, and 3 seniors on a school field trip. Three students are needed to carry water bottle cases. How many different ways can these students be selected?
Click here to see answer by ikleyn(52776)

Question 1116312: There are 4 freshman, 6 sophomores, 7 juniors, and 3 seniors on a school field trip. Three students are needed to carry water bottle cases. How many different ways can these students be selected if they must be all three freshman or all three juniors?
Click here to see answer by ikleyn(52776)

Question 1116299: Suppose a fair coin is tossed 12 times.
How many different sequences of heads and tails can result?
What is the probability that it will land heads exactly one time?
What is the probability that it will land heads at least one time?
Click here to see answer by Edwin McCravy(20054)

Question 1116370: How many different arrangements are there of the letters in MISSISSIPPI?
Click here to see answer by ikleyn(52776)

Question 1116457: 1. Find the number of possible 5-card hands that contain the cards specified. The cards are taken from a standard 52-card deck.
a) 4 kings and 1 other card.
b) At least 1 spade

Click here to see answer by stanbon(75887)

Question 1116461: 6. An arcade has 20 different arcade games. You want to play at least 14 of them. How many different combinations of arcade games can you play?

Click here to see answer by stanbon(75887)

Question 1116458: 2. Expand:
a) (y−3z)^5
b) (2s−t^4 )^4
I know she wants us to use paschals rule but I'm not sure how to do it without making the whole triangle can you explain how to find coefficients without making the triangle
Click here to see answer by greenestamps(13198)

Question 1116459: 4. Decide whether the problem requires combinations or permutations to find the answer. Then solve the problem:
Your school newspaper has an editor-in-chief and an assistant editor-in-chief. The staff of the newspaper has 12 students. In how many ways can students be chosen for these two positions?

Click here to see answer by greenestamps(13198)

Question 1116460: 5. Verify the identity. Justify your steps.
a) nC0 = 1
b) n+1Cr = nCr + nCr-1
c) nC1 = nP1

Click here to see answer by math_helper(2461)

Question 1116593: There are 8 cars plying between towns A and B. In how many ways can a person go from one town to the other and return by a different car?
Click here to see answer by greenestamps(13198)

Question 1115388: Prove that C(k,k)=1 for any value of k.
Click here to see answer by math_helper(2461)

Question 1116575: If 21st and 22nd term of the expansion (1+x)^44 are equal find the value of x

Click here to see answer by greenestamps(13198)

Question 1116644: How many distinguishable 6-digit numbers can be formed from the digits of 929219.

Click here to see answer by ikleyn(52776)

Question 1116694: N^p4=360
Find the value of n
Click here to see answer by ikleyn(52776)

Question 1116827: How many different 5-card poker hands contain exactly two kings?
I tried C(13,5) x C(4,2) x C(11,3) but I kept getting the wrong answer.
Click here to see answer by Theo(13342)

Question 1116852: Out of 5 Mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways can this be done if.
a) any mathematician and any physicists can be included
b) one particular physicist must be on the committee
c) 2 particular mathematicians cannot be on the committee
Click here to see answer by Boreal(15235)

Question 1117242: Find the number of ways of selecting 3 prefects in a class of 15 boys and 10 girls if one of the prefect must Be girl.
Click here to see answer by Fombitz(32388)

Question 1117248: Find the number of ways of selecting 3 prefects in a class of 15 boys and 10 girls if one of the prefects must be a girl.
Click here to see answer by Alan3354(69443)

Question 1117200: $n$ coins are simultaneously flipped. The probability that at most one of them shows tails is $\frac{3}{16}$. Find $n$.
Click here to see answer by greenestamps(13198)

Question 1117285: a university assinngs a 4 digit identification code what is the proabality that code doesn't contains 7?
Click here to see answer by ikleyn(52776)

Question 1117410: i) How many possible signals can be formed (e.g. 1st flag green, 2nd green, 3rd red, 4th
green, 5th blue, 6th blue, is one possible signal)?
ii) What is the probability that a signal formed will find the 6 flags in this configuration
(but not only in this order): 3 green flags, 2 blue and 1 red?
Click here to see answer by ikleyn(52776)

Question 1115154: There are 5 women and 4 men in a club, a team of 4 has to be chosen. How many different teams can be chosen if there must be either exactly one woman or exactly two women on the team?
Click here to see answer by math_helper(2461)

Question 1117622: What is the number of 3 digit numbers, with repeats, that are multiples of 5 and less than
600 that can be formed from the digits 1, 3, 5, 7, and 9?
Click here to see answer by solver91311(24713)

Question 1117681: How many arrangements of the word ECONOMICS begins with the letter C?
Click here to see answer by Edwin McCravy(20054)

Question 1117733: How many ways can 5 people A, B, C, D, E sit in a row if A must be to the left of B but not necessarily next to each other?
Click here to see answer by greenestamps(13198)

Question 1117775: There are 8 people A, B, C, D, E, F, G, H sitting in a row. If A must sit on the far left, and
B must be next to C, how many arrangements are possible?
Click here to see answer by rothauserc(4718)

Question 1117776: Three students were selected from a high school to run president, vice-president, and
secretary for student council. Three other students from the 38 middle school students were also selected to be on the council. What is the total number of ways that the 6 members of the student council can be selected?
Click here to see answer by ikleyn(52776)

Question 1117736: How many ways can 6 people work at 3 different offices if 2 people are in each office and 2
individuals refuse to work together?
Click here to see answer by ikleyn(52776)

Question 1117735: In how many ways can 12 jurors and 3 alternate jurors be selected from a group of 25 prospective
jurors?
Click here to see answer by stanbon(75887)

Question 1117811: Which term of is a constant?
Click here to see answer by solver91311(24713)

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