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

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Question 25279: Evaluate:
1*1!+ 2*2!+3*3!+.....+n*n! where n is in N
I started with if
n=1 then 1*1=1
n=2 then 1*1 +2*2*1=5
n=3 then 1*1 +2*2*1+3*3*2*1=23
............................
...........................
n=n then 1*1 +2*2*1+3*3*2*1+.....+n*n(n-1)(n-2)....3*2*1
the answer is (n+1)!-1 i can drive to this answer would you please help me.
Click here to see answer by venugopalramana(3286)

Question 26342: how many 6 number combinations will be made from 1 2 3 4 5 6 7 8 9, where 1 2 and 3 must appear on the 6-number combination?
Click here to see answer by venugopalramana(3286)

Question 28042: How many permutations are there for the letters in the word 'Kennebunk?'
Click here to see answer by stanbon(75887)

Question 28042: How many permutations are there for the letters in the word 'Kennebunk?'
Click here to see answer by venugopalramana(3286)

Question 28043: How many inversions are in the word 'Maine' if we assume that alphabetical order
is natural?
Click here to see answer by stanbon(75887)

Question 28044: If we select letters only one each from the word 'Kennebunk'how many permutations
are there?
Click here to see answer by stanbon(75887)

Question 28045: For work, I generally choose one of about five button down shirts,one of about 5 ties, one of about 3 pairs of pants, and one of 6 sports jackets. How many days could I go without wearing the samething (assuming I don't care if things match)?
Click here to see answer by stanbon(75887)

Question 28574: In combinations, does n necessarily have to be larger than p? Hint: try a test case.
Click here to see answer by venugopalramana(3286)

Question 29258: There are 10 players on a softball team. How many ways can the first 3 batters be chosen?

Click here to see answer by Nate(3500)

Question 31564: Find the number of different 5-card hands that can be dealt from a standard deck of 52 playing cards?
Find the probability that 4 kings and a queen are randomly drawn from a standard deck of 52 playing cards?
Click here to see answer by longjonsilver(2297)

Question 32083: How many arrangements of the word REVISITED are there with vowels not in increasing order and no consecutive E�s and no consecutive I�s?
(Normal order is a,e,I,o,u)
What i have done is by direct apporach and i have listed all the cases as prescribed and i got 20 cases in which each case has 5! distrubution of the remaining alphabets in between the specified directions. So the answer i am getting is 5!*20. I am not sure whtehr it is correct.
Thanks in advance.

Click here to see answer by venugopalramana(3286)

Question 32081: 4. How many arrangements are there of Seven a�s, Eight b�s, Three c�s, Six d�s
with no occurrence of the consecutive pairs ca or cc?
I have tried by indirect approach. The total cases being 24!/(7!*8!*3!*6!)
The bad cases being when ca or cc are together. I am getting stuck here as I don�t know whether the c I take in case ca should be counted again in cc.
Thanks in advance as I have been working on this question for a long time.
Click here to see answer by venugopalramana(3286)

Question 32642: Please help!
Given the set of numbers (77, 14, 21, 35, 42, ...) how can the 10th number be determined? I understand that the number 7 is divisible in each number given. But cannot determine the pattern to find the next 5 number's in the set? The question was given from the instrutor not by a textbook.
Thank you,
Bee
Click here to see answer by checkley71(8403)

Question 33528: 2v+3w=60 0.5v+4w=40 i need help solving it
Click here to see answer by mukhopadhyay(490)

Question 34558: Determine the number of combinations of 9 things taken 7 at a time.
Click here to see answer by stanbon(75887)

Question 34557: License plates are made by using 2 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed?
Click here to see answer by stanbon(75887)

Question 34555: A local department store sells carpets in 3 sizes. Each carpet comes in 2 different qualities. One of the sizes comes in 6 colors. The other sizes come in 2 colors. How many choices of carpet are there?
Click here to see answer by stanbon(75887)

Question 34556: A baseball manager has 11 players of the same ability. How many 9 player starting lineups can he create?
Click here to see answer by stanbon(75887)

Question 32302: A car door lock has a five-button keypad. Each button has two numerals. How many different five-button patterns are possible? (Hint: You can use a button more than once.)
Click here to see answer by stanbon(75887)

Question 30945: How do I solve this equation on a TI-83 calculator. x^4+5x^2+4=0 given that 2i is a root.
Thanks.
My test is tomorrow.
Click here to see answer by stanbon(75887)

Question 34706: Eight couples (husband and wife)are present at a meeting where a commitee of 3 is to be chesen . How many ways can this be done so that the commitee
a)Contains a couple? b)Cantains no couple?
Click here to see answer by stanbon(75887)

Question 34704: How many rearrangements of the letters in the word SUCCESS have the U before the E?
Click here to see answer by mukhopadhyay(490)

Question 35021: How do you know whether a word problem is a combination or permutation?
Click here to see answer by Prithwis(166)

Question 35191: How many ways can a committee of 3 can be picked from 6 students?
Click here to see answer by checkley71(8403)

Question 35193: How many different ways can 5 fruits be arranged in a picture using 3 fruits at a time?
Click here to see answer by stanbon(75887)

Question 35198: How many different salads made using 3 different fruits could be made from ten different fruits?
Click here to see answer by stanbon(75887)

Question 35892: You have 8 pictures to hang on a wall but you only want to hang 3 of them. How many ways can hang the 3 pictures from the eight? I came up with 56, am I doing this right?
Click here to see answer by longjonsilver(2297)

Question 36288: Can somone answer this problem?
The number of permutations of two items from a data set is always two times the number of combinations when taking two objects at a time from the same data set
Explain why this statement is true or false
Click here to see answer by stanbon(75887)

Question 36414: Question
In large data sets(1,000 or more values),the mean is always one of the data values. Why would this be true or false?
Click here to see answer by ilana(307)

Question 36413: Can you tell me if this is true or false
THe median of a data set is always one of the data values
Click here to see answer by ilana(307)

Question 37833: Can someone answer this and explain how it is done? Thanks
Joe remembered that the three digits in his locker combination were 3,5,and 7, but he forgot the order of the numbers. What is the maximum number of combinations he must check in order to open his lock? What are they?
Click here to see answer by longjonsilver(2297)

Question 37905: What is the difference between permutations and Combinations?
Click here to see answer by Alwayscheerful(414)

Question 38018: This problem i tried using probability distributions but i couldnot get
please help
Thanks in advance
A game consist of a sequence of plays on each play either you or your opponent scores a point, you with the probability p(less than �), he with probability q=1-p. The number of plays is to be even 2, 4, 6, etc� To win the game you must get more than half the points. You know p, say 0.45, and as you get a prize if you win. You get to choose the number of plays in advance How many should you choose?
Click here to see answer by fractalier(6550)

Question 38302: Divide
A. Use long division to divide x�+6x�-x-30 by x�+8x+15

B. Use synthetic division to divide (x�+5x�-18)/(x+3)
Click here to see answer by Nate(3500)

Question 38302: Divide
A. Use long division to divide x�+6x�-x-30 by x�+8x+15

B. Use synthetic division to divide (x�+5x�-18)/(x+3)
Click here to see answer by junior403(76)

Question 38354:
Can anyone answer this? There are two spinners, one is divided into thirds with green, yellow and blue. The second spinner is divided into fourths with blue, yellow, red and white. find the theoretical probability of spinning blue on both.

Click here to see answer by AnlytcPhil(1806)

Question 38372: I have two bags of marbles. One bag has a green, yellow and blue marble. The other bag has a blue,yellow,white and red marble. What is the probability of picking a blue marble from both bags?
Click here to see answer by fractalier(6550)

Question 38620: How many different license plate numbers can be made using 2 letters followed by 4 digits selected from digits 0 through 9 if letters and digits may be repeated?
Click here to see answer by venugopalramana(3286)

Question 38639: solve for x: 2x^2=13x+7
Click here to see answer by Nate(3500)

Question 38638: How many different arrangements of 9 letters can be formed from the letters in the word "SEVENTEEN" ?
Click here to see answer by Nate(3500)

Question 38637: How many different 6-digit numbers can be written using all of the following digits: 2,5,5,6,6,6 ?
Click here to see answer by Nate(3500)

Question 39197: i know the formula for permutations, but i don't know how to solve this problem. please help me!
joslyn's dance group consists of 8 girls and 5 boys. 4 people are to be chosen at random to perform at the next recital. if the group of performers must include at least 2 girls, in how many ways can the performers be chosen?
Click here to see answer by Nate(3500)

Question 39200: there are 12 people on kari's soccer team. individual pictures are taken and 8 pictures are selected to be hung in a row. how many different arrangements of pictures are possible if kari's picture must be among those hung?
Click here to see answer by hellyeah(21)

Question 39219: Please help me solve this:
Six hundred people are competing in a triathalon. there is a $1000 prize for first and a $500 prize for second. How many different first-second place finishes are possible?
I know the answer is 359,400, but i don't know how to solve it.
Click here to see answer by Nate(3500)

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