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

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Question 770152: members of a video club choose a PIN consisting of two letters and two digits.
How many PINs are possible if neither letter nor digits may be repeated?
Click here to see answer by John10(297)

Question 770104: how many different odd number of four digits can be formed with the digits 1,2,3,4,5,6,7.the digits in any number being all different?
Click here to see answer by oscargut(2103)

Question 770295: If a person is randomly selected, what is the probability that they have a birthday in March if they were born in 1988?
Click here to see answer by oscargut(2103)

Question 770295: If a person is randomly selected, what is the probability that they have a birthday in March if they were born in 1988?
Click here to see answer by Alan3354(69443)

Question 770299: A pixel in a digital image is represented by three primary colours red, green and blue in triples (R, G, B); each of which can take values from 0 to 255 (inclusive). For example,(255,0,0) represents the colour red and (100,145,75) represents a greenish colour.
How many different colours can a pixel represent?
Click here to see answer by Alan3354(69443)

Question 770496: To win the lotto jackpot you need to guess 6 numbers from a possible 49 numbers (from 1 to 49) with no replacement.
a) What is the probability of winning the Lotto?
b) If you have to pay R3.50 to play the lotto, what is the smallest amount for which it would be rational to play to the lotto, assuming that no one else picks the same set of numbers as you do?
Click here to see answer by stanbon(75887)

Question 770548: A security code used to consist of two odd digits, followed by four even digits. To allow more codes to be generated, a new system uses two even digits, followed by any three digits. If repeated digits are allowed, the increase in the number of possible codes is____
Answer: Old code: 5x5x5x5x5x5=15325
New code: 5x5x10x10x10=25000
The increase in the number of codes is 9375.
I don't understand why they use 5's and 10's!!!
Click here to see answer by solver91311(24713)

Question 770551: The number of three digit or four digit even numbers that can be formed from the numbers 2, 3, 5, 6, 7 is
Answer: 72
4 3 2 + 4 3 2 2 "I don't understand this, why they uses 4, 3, 2 and 4 3 2 2"
Click here to see answer by oscargut(2103)

Question 770599: using the digits0,1,2,3,4,5,6,7,8,9, how many 7 digit numbers can be formedif the first digit cannot be 0 or 9 and if the last digit is greater than or equal to 2 and less than or equal to 3? Repeated digits are allowed. how does the calculation look. Thanks
Click here to see answer by Edwin McCravy(20054)

Question 770591: In how many ways can n women be seated in a row so that 2 particular women will not be
next to each other?
Click here to see answer by Edwin McCravy(20054)

Question 770659: I have 64 people and need to make groups of 8 that will rotate 3 times and not be with the same person more than once.
Thank you.
Karen
Click here to see answer by Edwin McCravy(20054)

Question 770719: Dear Mr. McCravy - I posted my thank you publicly, but have another scenario.
What is we have 60 people and need to break them into groups of 6 with 4
rotations. I cannot get the same formula to work that way. Thank you for your
time. Karen
Click here to see answer by Edwin McCravy(20054)

Question 770757: how many different 10 letter words can be formed (real or imaginary)
a, u, e, f, o, k, u, l, l, h
Click here to see answer by Jc0110(165)

Question 770752: in how many ways can 7 people be seated at a round table if they can sit anywhere?

Click here to see answer by Jc0110(165)

Question 770763: How many words of length 10 can be formed if all five vowels are adjacent and any 5 consonants are used?

Click here to see answer by Jc0110(165)

Question 770750: In how many ways can 7 people be seated at a round table if they can sit anywhere and 2 particular people must not sit next to each other?

Click here to see answer by Jc0110(165)

Question 770762: how many words of length 10 can be formed using any 5 consonants and all of the vowels. vowels must be adjacent.

Click here to see answer by Jc0110(165)

Question 771008: How many groups of 6 boys and 5 girls can be found from 10 boys and 7 girls?
Click here to see answer by Jc0110(165)

Question 769197: In how many ways can 7 boys be arranged in a row if the shortest and the tallest boy are separated?
Click here to see answer by Jc0110(165)

Question 771177: In how many ways can 7 athletes be arranged in a straight line?
Click here to see answer by Jc0110(165)

Question 771182: how many 2 digit numbers and single digit numbers can you get out of a 7 digit number, in a set of 6 numbers consisting of both single and double digit numbers with the highest number being 59 and the lowest number being number 1 using addition, and multiplication,subtraction
Click here to see answer by Edwin McCravy(20054)

Question 771267: solve the equation P(n,5) = 20P(n,3) for n
Click here to see answer by oscargut(2103)

Question 771272: In an examination there are three multiple choice questions and each question has 4 choices. In how many number of ways a student can fail to get all answers correct?
Click here to see answer by oscargut(2103)

Question 771281: In how many ways can 5 prizes be distributed among 4 boys when every boy can take one or more prizes?
Click here to see answer by oscargut(2103)

Question 771713: in a cricket championship there are 36 matches. the number of teams if each plays one match with other are ?
Click here to see answer by oscargut(2103)

Question 771722: In a company, out of the 7 applicants for 3 positions, 3 are males and 4 are females. In how many ways will 3 females be chosen? Thank you.
Click here to see answer by oscargut(2103)

Question 771723: In a company, out of the 7 applicants for 3 positions, 3 are males and 4 are females. In how many ways will 1 males and 2 female be chosen? Thank you.
Click here to see answer by oscargut(2103)

Question 771724: In a company, out of the 7 applicants for 3 positions, 3 are males and 4 are females. In how many ways will 3 male be chosen? Thank you.
Click here to see answer by oscargut(2103)

Question 771725: Combination(solution)-the college food plan allows a student to choose three pieces of fruit each day.The fruits available are apples,bananas,peaches,pears and plums.for how many days can a student make a different selection?
Click here to see answer by oscargut(2103)

Question 771734: How many groups of 4 people can be formed from 6 people?
Click here to see answer by oscargut(2103)

Question 771733: My problem is (11!)/ (4!)(4!)(2!)
The book says that the next step is
11�10�9�8�7�6�5�4! / (4!)(4!)(2!)
How did they get that and how do I enter this into my calculator?
Click here to see answer by MathLover1(20849)

Question 771868: until recently U.S. telephone area codes were three-digit numbers whose middle digit was 0 or 1.codes whose last two digitsw are 1's are used for other purposes(for example,911).with these conditions how many area codes were available?

Click here to see answer by oscargut(2103)

Question 771895: give a procedure for determining the number of zeros at the end of n!.justify your procedure.
Click here to see answer by Edwin McCravy(20054)

Question 771875: how many social security numbers can be assigned at any one time?identify any assumptions you have made.

Click here to see answer by Alan3354(69443)

Question 772059: There are 15 women and 12 men in a room, none of whom you have met. how many people must you meet to be sure of meeting two men?
Click here to see answer by Edwin McCravy(20054)

Question 772145: How many numbers greater than 6000 and less than 7000 can be formed without repetition if the number is divisible by 5 ?
Click here to see answer by Edwin McCravy(20054)

Question 772472: How many permutations of the digits 0, 1, 2, . . . , 9 either
start with a 3 or end with a 7?
Click here to see answer by Edwin McCravy(20054)

Question 772496: what exactly is distinguishable permutations

Click here to see answer by solver91311(24713)

Question 772808: Will the number of permutations always be greater than the number of distinguishable permutations? why or why not?
Click here to see answer by stanbon(75887)

Question 773121: 2,6,10,14,18, 22, 26, 30, 34, 38 which five letter grand total is 100

Click here to see answer by Edwin McCravy(20054)

Question 773181: How many ways can a group of 7 people be chosen from a class of 15?
Click here to see answer by jim_thompson5910(35256)

Question 773277: 3eDSABDA RWHGVDARGRH5XH Z
Click here to see answer by ramkikk66(644)

Question 773341: A teacher chooses 3 students from a group of 14 to explain their project. In how many ways can she choose 3 students? Answers are: a. 228 b. 364 c. 1082 or d. 2184.
Click here to see answer by Edwin McCravy(20054)

Question 773458: Helen has four jogging outfits and three pairs of shoes. How many different outfits can she make?
Explain fully. Help please. Make me understand so I can explain to others.
Click here to see answer by josmiceli(19441)

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