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

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Question 924969: three out of four students made an A on the last test. If there are 32 students , how many made an A
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Question 925067: How many ways u can select 11 members of team from 15 members
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Question 925311: How many license plates of 5 symbols can be made using a letter for the first symbol and digits 0-9 for the remaining 4 symbols?
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Question 925296: A catering service offers 10 appetizers, 11 main courses, and 8 desserts. A banquet chairperson is to select 7 appetizers, 8 main courses, and 4 desserts for a banquet. In how many ways can this be done?
Click here to see answer by ewatrrr(24785) About Me 

Question 925549: a clubs members are 7/9+ girls and 8 (the rest) are boys. How many members are there?
Click here to see answer by rfer(16322) About Me 

Question 925666: License plates with two letters followed by four digits (0 - 9)
Click here to see answer by Alan3354(69443) About Me 

Question 925797: If 3 melons sell for $0.42, how much would 7 melons cost?
Click here to see answer by TimothyLamb(4379) About Me 

Question 925983: In how many ways can 4 large books, 3 medium- size books, and 2 small books, be placed on a shelf so that all books of the same size are together
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Question 925808: How many 8 character passwords are possible if characters cannot be repeated and they must feature both numbers and letters. Letters are not case sensitive so there are only 36 possible characters.
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Question 926075: how many 3-digit codes can be created if the first digit can be any letter of the alphabet, and the next two digits must be odd numbers?
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Question 926047: Q= how many possible committees can be formed from a group of seven people if each committee can have any number of member from 1 to 7?
the answer given is 127, solution pls

Click here to see answer by stanbon(75887) About Me 

Question 926313: A club has 50 members.

a) How many ways are there to choose four members of the club to serve on an executive committee?

[Num] ways

b) How many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office?

Click here to see answer by ewatrrr(24785) About Me 

Question 926347: employees must have an exactly 8 character password. How many different passwords exist if they can only use the numbers 0...9 (no symbols, no letters). Note repetition is allowed.
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Question 926385: there are 10^6 personal identification numbers. There are 7x10^5 people who will be assigned a PIN. How many PIN numbers are available for each person?
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Question 926475: Hi guys, i was wondering if someone could help me with the following question. I cant seem to work out the answer :(( Thanks!
Q: In how many ways can 12 toys be divided evenly between 3 children

Click here to see answer by LOL MASTER(6) About Me 

Question 926588: In a cinema there are 10 rows with each row having 25 seats. The seats are numbered. If two friends buy tickets for themselves without knowing each other, what is the probability that they'll sit next to each other?
Click here to see answer by josmiceli(19441) About Me 

Question 926629: A coin is tossed with possible outcomes H or T. Then a spinner spun with possible outcomes 1 through 4; draw a tree diagram and list the combined outcomes. What is the probability of rolling an odd number and a tail?
Click here to see answer by stanbon(75887) About Me 

Question 926858: 7 different dishes are being served for thanksgiving. How many different dinner combinations are possible if each has 4 dishes?
Click here to see answer by ewatrrr(24785) About Me 

Question 926890: In statistics class of 24 students , a students , a 5 person committee is to be chosen. How many ways can this be done ?
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Question 927117: How many different committees of 4 members can be formed from a group with 7 seniors and 6 juniors if they are 3 seniors and 1 junior?
Click here to see answer by Edwin McCravy(20054) About Me 

Question 927161: In a group of 14 students, there are 8 girls and 6 boys.
a) Determine the number of ways that a committee of 4 students can be chosen from this group.
b) Determine the number of ways that a committee of 4 students which has exactly 2 girls can be chosen from the group.
c) Determine the number of ways that a committee of 4 students which has at least 1 boy can be chosen from the group.
d) The committee of 4 students must have 1 girl, 1 boy , and 2 other students, how many different committees can be chosen from this group?
I have solved a), b) and c) for the question, but I am not sure about d).
I thought maybe it could be worked out like this:
8C1 x 6C1 x 12C2 = 3,168
I don't know if that is right though. Any help would be greatly appreciated. Thank you!

Click here to see answer by ewatrrr(24785) About Me 
Question 927161: In a group of 14 students, there are 8 girls and 6 boys.
a) Determine the number of ways that a committee of 4 students can be chosen from this group.
b) Determine the number of ways that a committee of 4 students which has exactly 2 girls can be chosen from the group.
c) Determine the number of ways that a committee of 4 students which has at least 1 boy can be chosen from the group.
d) The committee of 4 students must have 1 girl, 1 boy , and 2 other students, how many different committees can be chosen from this group?
I have solved a), b) and c) for the question, but I am not sure about d).
I thought maybe it could be worked out like this:
8C1 x 6C1 x 12C2 = 3,168
I don't know if that is right though. Any help would be greatly appreciated. Thank you!

Click here to see answer by stanbon(75887) About Me 

Question 927165: BC Place Stadium has 16 gates. In how many ways can you enter the stadium and leave the stadium:

a) by a different gate
b) by any gate
Thank you for the help!

Click here to see answer by Fombitz(32388) About Me 

Question 927095: How many different committees of 4 members can be formed from s group with 7 seniors and 6 juniors if they are 3 seniors and 1 junior?
Click here to see answer by ewatrrr(24785) About Me 

Question 927398: find the number of ways in which the letters of the word (grilled) can be arranged if
i.The two 'll' must not come together.
ii. The two 'll' are together

Click here to see answer by Theo(13342) About Me 

Question 927431: Which term in the expansion of (1/(2x^3) - x^5))^8 is a constant?
I know you expand it into the equation

= (nCk) a^(n-k) b^k
to get = 8Ck (1/(2x^3))^(8-k) (-x^5)^k
but I am not sure what to do after that.
Thank you for the help!

Click here to see answer by richard1234(7193) About Me 
Question 927431: Which term in the expansion of (1/(2x^3) - x^5))^8 is a constant?
I know you expand it into the equation

= (nCk) a^(n-k) b^k
to get = 8Ck (1/(2x^3))^(8-k) (-x^5)^k
but I am not sure what to do after that.
Thank you for the help!

Click here to see answer by Edwin McCravy(20054) About Me 

Question 927389: In how many ways one or more than one questions can be answered out of 6 questions , each questions has one alternative
Click here to see answer by ewatrrr(24785) About Me 

Question 927510: How many numbers multiples of 5 greater than 20 000 can be made from the following digits: 0,1,3,5,7,9?
My answer:
6^3*7 + 6^4*9
I'm not sure! Please help!

Click here to see answer by Alan3354(69443) About Me 

Question 927564: How many possible combinations are there in a 5000 diget password?
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Question 927610: Find the number of ways of seating 3 men and 5 women in a row if there is no restriction
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Question 927624: In how many ways k types of work can be assign to n workers so that everyone has exactly
one job?

Click here to see answer by Edwin McCravy(20054) About Me 

Question 927615: 5 letters from the word "DRILLING" are arranged in a row.
I.Find the number of way in which this can be done, when the first letter is "I" and the last letter is "L".
a.If no letter maybe repeated.
b.If each letter occurs as many time as it does in DRILLING

Click here to see answer by Edwin McCravy(20054) About Me 

Question 927446: Three ladies have each brought a child for admission. The head of the school wishes to interview the six people in such a manner that no child is interviewed before his/her mother. What are the no. of ways of doing this?
Click here to see answer by Edwin McCravy(20054) About Me 
Question 927446: Three ladies have each brought a child for admission. The head of the school wishes to interview the six people in such a manner that no child is interviewed before his/her mother. What are the no. of ways of doing this?
Click here to see answer by richard1234(7193) About Me 

Question 927305: Which term in the expansion of ((1/2x^3) - x^5))^8 is a constant?
I know you put it into the equation t (k+1) = (nCk) a^(n-k) b^k to get:
= 8Ck (1/(2x^3))^(8-k) (-x^5)^k
But I don't know what to do after.
Thank you for the help!

Click here to see answer by Edwin McCravy(20054) About Me 

Question 926855: There are 12 different colored PAIRS (24 socks total, 12 different colors) of socks in a drawer. If a person takes 10 socks from that drawer, what is the probability that none of these socks are pairs?
Click here to see answer by Edwin McCravy(20054) About Me 

Question 927516: Eight plates are stacked in three piles with two piles of three plates each and one pile of
two plates. You are to pick up the plates one at a time following these rules:
1) You first choose a pile from which to pick up a plate.
2) You must then pick up the top plate from that pile.
By following these rules, in how many different orders can you pick up the eight plates?

Click here to see answer by Edwin McCravy(20054) About Me 

Question 927204: A van has 3 bench seats holding 3 people per bench. 9 passengers are going to get in the van: a couple, 3 family members, and 4 random people. The 3 family members will only go if they sit together on one bench and the couple will only go if they sit side by side. How many ways are there to arrange these passengers?
My answer: 5,120

Click here to see answer by Edwin McCravy(20054) About Me 

Question 927667: a) In how many ways can a committee consisting of three men and two women be chosen from seven men and five women?
b) How many committee of five with a given chairman can be selected from twelve persons?
c) In how many ways can a teacher choose one or more students from six eligible students?
d) Find the number of permutations that can be formed from the letters UNUSUAL?

Click here to see answer by Edwin McCravy(20054) About Me 

Question 927195: There are 6 boys and 18 girls in a class. A group of 5 students is needed to work on a project. If at least 2 boys are needed, how many different groups of 5 students are possible?
Click here to see answer by Edwin McCravy(20054) About Me 

Question 926976: In how many ways can 12 toys be divided evenly between 3 children
?

Click here to see answer by Edwin McCravy(20054) About Me 

Question 927094: How many different committees of 4 members can be formed from s group with 7 seniors and 6 juniors if they are all seniors?
Click here to see answer by Edwin McCravy(20054) About Me 

Question 927630: In how many ways can be done the allocation of n groups of students for k assistants, if (k-1)
of assistants shall select two groups and the k-th - the rest of them.

Click here to see answer by Edwin McCravy(20054) About Me 

Question 927628: We have n colors of paint. How many mixtures of k different colors can we compose?
Click here to see answer by Edwin McCravy(20054) About Me 

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