Tutors Answer Your Questions about Permutations (FREE)
Question 943951: a computer password must be 5 characters long. the first character must be a capital letter. the second character must be a digit from 0 through 9, inclusive. the third character must be one of eight specified symbols. each of the fourth and fifth character can be any combination of capital or lowercase letters, digits or symbols. where the symbols are from the 8 specified symbols. how many different passwords can be made using these rules?
possible ans:
(A) 1,274,000
(B) 2,548,000
(C) 5,096,000
(D) 10,192,000
(E) 40,768,000
Click here to see answer by Edwin McCravy(20054)   |
Question 943193: A class consists of 12 girls and 18 boys. A president, vice-president and treasurer are chosen based on the number of votes. Find the probability of selecting a president, vice-president and treasurer where all 3 are different boys from the class.
Click here to see answer by Edwin McCravy(20054) |
Question 942185: Q.3 Find a particular solution to the recurrence.
an+1 − 2an + an−1 = 5 + 2n, n ³ 1(15 marks) plz send full solution
Q.5 (a) If R = {(1, 1), (2, 1), (3, 2), (4, 3)}, find R2,R4.
(b) How many permutations are there of the letters, taken all at a
time, of the word ALLAHABAD?(7,7marks) plz send full solution
Q.6 Let A = {0, 1, 2, 3} and R = ((x, y) : x − y = 3k, k is an integer) i.e,
XRy if f x-y is divisible by 3, then prove that R is an equivalence
relation
Click here to see answer by Edwin McCravy(20054) |
Question 941398: What is the number of ways letters in the word KOMBINATOORIKA can be rearranged, such that no two consecutive letters are the same?
(the correct answer should be 710579520, not 100% sure though)
I tried first ordering 5 letters and then placing letters K in 6C2 ways, then A in 8C2 ways...etc, but with O-s it would make it different on when i select the three positions for them(whether 6C3,... or 6C2,8C2,11C3...), because i would need to multiply them at the end.
Also tried applying inclusion-exlcusion, but was unable to make it work.
Click here to see answer by Edwin McCravy(20054) |
Question 944504: (a) From the 13 albums released by a musician, the recording company wishes to release 9 in a boxed set. How many different boxed sets are possible?
(b) How many different committees of size 3 can be formed from 13 people?
This is the problem that I am working on. I was wondering how you determine which equation to use (the one for permutations or the one for combinations). The explanation for similar problems say that to use the permutation equation, the order does not need to matter. However, for the combination equations, the order does matter. So my question is, in a problem like the one stated above, how do you determine whether or not the order of the numbers matter?
Click here to see answer by Edwin McCravy(20054) |
Question 945384: 1)A person has two sons and two daughters. There are three boys' schools and two girls' schools in the area where they lives.In how many different ways can the children be sent to school?In how many ways can the children be sent to school such that no two children attend the same school?
2)A shirt factory produces shirts of three different sizes. It is expected to produce shirts with two different materials and four different colors for the festive season. How many different shirts can be produced?
3)Find the number of all positive numbers with not more than four digits that can be made using the digits 0,1,2,3,4 and 5. Find also the number of numbers out of these in which each digit is not repeated.
Click here to see answer by Edwin McCravy(20054) |
Question 945151: Suppose that three fair dice are thrown. Compute the probability of the following events:
(a) the event is ‘big’, that is, the sum of the three dice is at least 10 but the three dice
do not show the same value;
(b) the event that the sum is 13;
(c) the event that a specific combination of two different numbers appears, e.g. {3, 4}
appears.
Click here to see answer by Edwin McCravy(20054) |
Question 945535: A company is composed of 5 senior executives, 10 executives and 5 senior managers. A 5 person committee is formed to attack a particular issue.
How many different 5 person committees are possible?
C(20,5) =20!/(20-5)!5!=(20!5*4*3*2*1)/15!=(20*19*18*17*16*15!)/(15!*5*4*3*2*1)=1860480/120=15504
If the committee must be composed of 2 senior executives, 2 executives and 1 senior manager, how many different 5 person committees are possible?
Click here to see answer by jim_thompson5910(35256) |
Question 945526: 1)Alan has 5 pairs of trousers and 6 shirts. Ben has 7 pairs of trousers and 4 shirts. Who has the most choice of what to wear? Why?
2)From the digits 0, 1, 2, 3, 4, 5, how many 4-digit even numbers with distinct digits can be formed? (Hint: Consider two cases: when it begins with 1, 3 or 5 and when it begins with 2 or 4)
3)Morse code is made from dots and dashes. The letter E is a dot (using 1 character), the letter N is a dash followed by a dot (using 2 characters), the letter S is three dots (using 3 characters). Explain why it is possible to construct the 26 letters of the alphabet using maximum 4 characters.
4)5 cards are selected randomly from a packet of 52 cards (there are 4 suits in the packet, and each suit has 13 cards). In how many ways can at least 4 cards of the same suit be selected?
5)3 girls and 4 boys sit in a row for a photograph. Find the number of ways they can be seated if
(a) the 3 girls sit together.
(b) no girls sit together.
(c) only 2 of the girls sit together.
(d) the 3 girls sit in alphabetical order, from left to right, but not necessarily together.
(e) girls and boys alternate, where the tallest girl sits in the middle.
Click here to see answer by Edwin McCravy(20054) |
Question 944565: A student has 5 engineering books, 3 math books, and 4 chemistry books. She is to put them all onto three shelves (top, middle, lower) with each shelf containing only books of a single discipline, but the order on any particular shelf is completely free. In how many ways can she do this ?
I'm stuck here, it seems easy enough, but why would the number of books matter if each shelf contains one discipline and the order on each shelf doesn't matter? Am I missing something here?
It looks along the lines of 5!*3!*4!*3!, but not sure.
Click here to see answer by Edwin McCravy(20054) |
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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
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