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

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Question 413523: Four-Digit Number. How many four-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed.

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Question 413597: what is the answer to the permutation 12p10

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Question 413597: what is the answer to the permutation 12p10

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Question 413817: Can I get validation on my first part of the problem and help with the second half. I would greatly appreciate it.
A gargae door opener has a sequence of 10 switches, each switch has 3 positions (0,1,2).
a.) how many codes are possible with these switches.
C(10,3)= 720
b.)how many of these codes have exactly 4 twos and exactly 4 ones in them?
thanks,
Gina

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Question 414169: I was wondering if someone could tell me if I got these problems right? I am finding this to be a difficult subject.
A pin consists of 2 letters followed by 3 numbers (assume repetition is allowed and order is important).
a) how many different pin numbers are there?
26*26*10*10*10=676,000
b) what is the proabilty a pin number selected randomly ends in 000?
26*26*9*9*9=492,804
c)what is the probability a pin selected at random begins with AA?
25*25*10*10*10=625,000
d)what is the probability a pin selected at random being with A and ends with 00?
25*26*10*9*9=526,500
e)what is the probability a pin selected at random has a repeated letter and different numbers?
26*25*10*9*8=468,000

Thanks for your time and help,
Gina

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Question 414341: A math quiz has one multiple-choice questions with the answers a,b,c and two true/false questions. What is the probablity of answering all the questions right by guessing?
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Question 414700: in how mant ways can 3 identical emeralds, 2 identical diamonds and 2 different opals be arranged in a row in a display case
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Question 414739: how many ways can 9 students (5 girls and 4 boys) be seated in a row if seatings must alternate boy then girl? or girl then boy?
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Question 415068: how many ways can 5 different books be distributed amongst 10 persons,assuming a person can get any amount of books?
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Question 415610: in how many ways can 4 boys and 3 girls be seated in a row of 7 seats if end seats are to be occupied by boys

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Question 415616: how many permutations can be made from selecting 4 college courses out of 10

and i had some trouble understanding,
four students can choose to write on one of 5 essay topics for their english class .
how many different essays can the student write without repetition of the topics?
how many different essays can the student write with repetition of the topics?

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Question 415904: 120 numbers can be made from digits 1,2,3,4,5 if each digit is used once in a number. The smallest number is 12345 and the largest is 54321. If the 120 numbers are listed in order from smallest to largest, what is the 73rd number in the list?
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Question 416508: There are 17 math team members, they must pick five members to go to regional how many combinations are possible? A.170 B.12,376 C.85 D.6188
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Question 416508: There are 17 math team members, they must pick five members to go to regional how many combinations are possible? A.170 B.12,376 C.85 D.6188
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Question 416531: From 250 lottery tickets that are sold, three tickets are to be selected for first, second, and third prizes. How many possible outcomes are there?


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Question 416530: Find the number of all the ordered arrangements of 6 objects a, b, c, d, e, and f, choosing 4 at a time without repetition.

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Question 416541: How many nine-bit strings contain exactly seven 1s?

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Question 416529: How many five-digit numbers can be formed using the digits 0 and 6? Repeated digits are allowed.
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Question 416693: a company manufactures a television which is found to have a 10% probability of being defective in some way. a sample of 4 televisions is taken.
1) what is the probability that exactly 1 television will be defective?
2) what is the mean of this distribution?
3) what is the standard deviation of this distribution?
having issues with these three problems, thank you

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Question 416849: a box contains 12 quarters and 12 dimes. when the box is turned upside down, two coins fall out at once. the size of the coin has no effect on its probability of falling out of the box.
1) what is the probability that 2 dimes fall out?
2)what is he probability that one dime and one quarter fall out?

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Question 416817: in how many ways can 8 girls line up in a row if 3 refuse to separate?
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Question 416862: If you have 20 cds in your collection at home, and your select 5 cds to play in your car. how many combinations of 5 cds can be made from your collection?
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Question 416926: How many 5 digit zip codes are possible if 00000 is not used? Thanks Denise
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Question 416926: How many 5 digit zip codes are possible if 00000 is not used? Thanks Denise
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Question 417388: Find how many 4 digits number are even and how many 4 digits number are odd.
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Question 417279: In how many different ways can the startig five players of a basketball team stand in a row for a picture?
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Question 417733: There are 10 buses. In how many ways can 5 people be assigned to each vehicle if they have to ride on different buses?
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Question 417822: Suppose there are 12 applicants for the same job. In how many ways can 8 of them be selected and scheduled for interviews on the same day, one each hour from 9a.m. to 4.p.m.?
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Question 417825: A person has 1 brother and 8 cousins. She has a photograph of each person. In how many different ways can she display the photographs in a row if her brother's photo must be right in the middle?
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Question 417824: How many binary strings of length 9 start and end in 0?
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Question 417856: I am hoping I can get some help with this problem be cause it just doesn't seem right to me.
rounded to the 4th decimal
C(5,5)/C(25,5)
1/53130=.0000
????
Thanks,
Dave

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Question 417821: Suppose that you have six different vegetables in the refrigerator. In how many ways can you choose four of them to put into your salad?
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Question 417914: Solve. C(6,3)
This is what I have tried. 6!/3!*3= 720/18=40
I am not sure if this is correct.

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Question 417930: How many different arrangements can you make with the letters in the word, Mississippi?
This is what I have tried:
11!/4!*4!*2!= 39,916,800/1152=34,650
Is this correct?

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Question 417988: Using the letters MAMMAL find:
a) how many different ways to arrange the letters
b) If we insist that the letter M come first and last, how many ways are there?

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Question 418040: I can't seem to figure this one out. It's a combination question I think. Here is the question, "A costruction supervisor needs a crew of 14 to do a job, and 15 people voluteered. How many 4- person crews can be chosen?" I hope you can help. Thank you
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Question 418042: I keep on finding difficulty in Combinations and Premutations. Here is one question, "In how many ways can 9 people be lined up if 2 of them insist they must stand next to each other?"
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Question 417989: An experiment consists of flipping a fair coin 8 times, how many ways can this experiment result in at most 2 heads?
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Question 418179: How many odd 6-digit pin numbers can be made from the digits 0-9?
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Question 418179: How many odd 6-digit pin numbers can be made from the digits 0-9?
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Question 418553: determine the number of subsets of a set containing of 8 members.
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Question 418544: The probability that both Vic and Jim can solve the same problem is 19/20. The probability that Vic can solve the problem is 49/50. What is the probability that Jim can solve the problem given that Vic can?
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Question 418549: In how many distinguishable ways can letters of the word TENNESSEE be arranged?
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Question 418552: A manufacturer of houses has 1 floor plan but achieves variety by having 3 different roofs, 4 different ways of attaching the garage, and 3 different types of entrances. Find the number of different houses that can be produced.
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Question 418566: How many different 7-place licence plates are possible if the first 3 places are occupied by letters and 4 by numbers.
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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