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

Tutors Answer Your Questions about Permutations (FREE)

Question 939958: How many 5 letter-words using letters from TRIANGLE can be made if the five-letter word must have two vowels and three consonants?
I set up the question using 5 blank spaces and wrote it like this:
5 4 3 3 2
then I multiplied
and I got 360 different 5 letter words.
answer key says 3600, where did I go wrong?

Click here to see answer by Edwin McCravy(20054)

Question 939752: Using the letters QRSTUVWXYZ, how many different arrangements could be made if X,Y, or Z must come first?
Thanks a ton for the help!
-Isaac
Click here to see answer by Edwin McCravy(20054)

Question 940083: Out of 500 students investigated, 400 studies Hindi, 200 English and 50 both. Is this data correct.
Explain and justify your answer.

Click here to see answer by krutarthas(22)

Question 940082: A group consists of 4 girls and seven boys. In how many ways can a team of 5 members be selected if the
team has (i) no girl (ii) at least one boy and one girl. (iii) At least 3 girls.

Click here to see answer by Edwin McCravy(20054)

Question 940084: Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and
B. Is this data correct? Explain.
Click here to see answer by Edwin McCravy(20054)

Question 940084: Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and
B. Is this data correct? Explain.
Click here to see answer by ewatrrr(24785)

Question 940152: _+_+_+_+_=30
Click here to see answer by Edwin McCravy(20054)

Question 937214: In how many ways can a person get a bridge hand consisting of only aces or faces cards?Please help me to solve this question.
Click here to see answer by Edwin McCravy(20054)

Question 940228: Prove that the following relationship is true:
nCr + nC(r+1) ?=? (n+1)C(r+1)
Use the least common denominator method.
Click here to see answer by Edwin McCravy(20054)

Question 940602: The final score of a hockey game is 4 to 3. How many different scores could there have been at the end of the first period?
Answer is 14, but I don't know how to get it.
Click here to see answer by stanbon(75887)

Question 939432: Prove that 6C2 + 6C3 = 7C3
Step 1 6! 6!
--- + ---
2!4! 3!3!
Step 2 6! 4*6!
---- + -----
4*3!3! 4*3!3!
Step 3 5*6!
------
4*3!3!
Step 4 7! 7*6!
---- = -----
3!4! 4*3!3!
Step 5 5*6! 7*6!
----- not equal -----
4*3!3! 4*3!3!
Click here to see answer by Edwin McCravy(20054)

Question 940582: In selecting an ace;king;queen;and jack from an ordinary deck of 52 cards;how many ways may we choose if (a)they must be of different suits;(b)they may or may not be of different suits;(c)they must be of the same suit;(d)they must be in a particular suit?Please help me to solve this question.
Click here to see answer by Edwin McCravy(20054)

Question 931738: In how many ways may a factory manager assigns one or more of her 7 workers to undergo a screening test?
Click here to see answer by Edwin McCravy(20054)

Question 940589: A baseball manager insists on having his best hitter bat fourth and the pitcher bat last.In such circumstances;how many batting orders are possibles?Please help me to solve this question.
Click here to see answer by Edwin McCravy(20054)

Question 940504: a restaurant menu lists 5 appetizers, 6 main dishes and 4 desserts that are specialties of the house. Each day the restaurant offers a combinations of one of each at a special price. For how many consecutive days can the restaurant offer these combinations without repeating the same one?
Click here to see answer by Edwin McCravy(20054)

Question 940452: airtel wants to make mobile phone numbers consisting of the
digits 0,1,2,3,4,5,6,7,8 and 9 how many numbers are possible if: i.The first digit is 0 and they are to consist of only eight digits?
Click here to see answer by Edwin McCravy(20054)

Question 940375: In how many ways can I divide a group of 12 persons (n = 12) into four subgroups (k = 4) of at least 2 persons (l=2)?
Click here to see answer by Edwin McCravy(20054)

Question 940085: A ray of light passing through the pont (1,2) reflects on the x axis at point A and the reflected ray
passes through the point (5,3) find the corrdinates of A.
Click here to see answer by Fombitz(32388)

Question 941085: n number of red coins, blue coins and green coins are present in a bowl, your eyes is closed.How many attempt you required to choose two coins of same color?
Click here to see answer by richard1234(7193)

Question 941328: four digit number which is ascending and their combination to be 21
please send me the combination of such four digit no's
Click here to see answer by Fombitz(32388)

Question 941564: a restaurant offers 6 different salads 5 different main courses 10 different desserts and 4 different drinks. how many different lunches each consisting of a salad, a main course a dessert and a drink are possible
Click here to see answer by srinivas.g(540)

Question 941728: The word EQUATIONS contains all five vowels. How many 7-letter "words" consisting of all five vowels can be formed from the letters of EQUATIONS?
Thanks!!
Click here to see answer by stanbon(75887)

Question 146045: What is the difference between a Permutation and a Combination?

Click here to see answer by Kamil Ashraf(1)

Question 941751: How many numbers are possible from the set {0, 1, 2, 3, 4, 5, 6, 7} if:
a) the numbers must be less than 500?
b) the numbers must be odd?
c) the numbers must be even?
Click here to see answer by Edwin McCravy(20054)

Question 942235: Evaluate the expression.
(10) (6) (3)
7 4 1
Click here to see answer by Alan3354(69443)

Question 942234: A state's license plates consist of three letters followed by three numerals, and 242 letter arrangements are not allowed. How many plates can the state issue?
Click here to see answer by Alan3354(69443)

Question 942820: using the digits of 0,1,2,3,4,5,6,7,8,9 determine how many 3 digits numbers can be constructed according to the following criteria zero cannot be used for the first digit, digits may repeat
Click here to see answer by stanbon(75887)

Question 942850: what is the formula for permutation in algebra 1
Click here to see answer by Theo(13342)

Question 942893: a lady picked up five new tops, four skirts, and three new pairs of shoes. How many different combinations can the lady make with
her new clothing items?
Click here to see answer by richard1234(7193)

Question 943195: Two playing cards are dealt to you from a well-shuffled standard deck of 52 cards. If either card is a diamond or if both are diamonds, you win; otherwise, you lose. Determine whether this game favors you, is fair, or favor the dealer. Explain your answer.
Click here to see answer by Edwin McCravy(20054)

Question 942971: A person is creating a dinner menu for the party. he can choose from 3 appetizers, 4 main courses and 2 desserts.
How many different meals are possible?
Please if you could explain the mathematical way of doing this.
Thanks
Click here to see answer by Edwin McCravy(20054)

Question 942561: Using all the prime numbers less than 10 how many four-digit even numbers can be made if repetition is not allowed?
Click here to see answer by Edwin McCravy(20054)

Question 943261: A Dudley-brand lock is made of a 60-number dial (0, 1, 2, . . . , 59). To unlock it, one
must make the right sequence of 3 numbers in order. Turning the dial to clockwise to
the first number, then counterclockwise (a full turn and then continuing) to the second
number, then clockwise to the third number. There are conditions that a number
cannot be used twice in a row, and the next number cannot be one of the 2 immediate
neighbours (one to the left, one to the right). How many possible different arrangements
are there for a Dudley lock? (For example 59, 1, 59 is a possible arrangement.)
Click here to see answer by Fombitz(32388)

Question 943372: College randomly assigns students to 5 dorms. if 3 friends apply to live in these dorms, what is probability they are assigned to same dorm? What is probability they are assigned to different dorms?
Click here to see answer by Edwin McCravy(20054)

Question 943515: your closet contains five ties and seven shirts. how many different outfits can you create
Click here to see answer by stanbon(75887)

Question 943559: A three digit number uses the numbers 1, 5, and 7. any number can be repeated in the three digit number. how many three digit numbers are possible?
Click here to see answer by stanbon(75887)

Question 943593: my question is- There are 5 items in a bag. How many ways can you pick 1 item from the bag at once? - I have tried everything but nothing worked to get the right answer
Click here to see answer by Alan3354(69443)

Question 943417: How many four-letter arrangements can be made using the letters {a, b, c, d, e} if repetitions are allowed, but no letter may follow itself?
Click here to see answer by Edwin McCravy(20054)

Question 943571: How many 5 letter arrangements can be made using the letters in the word INDEPENDENCE

Click here to see answer by Edwin McCravy(20054)

Question 943342: A voice teacher selects 9 students from the class to sing for the trustees. The class has 12 men and 13 women. In how many ways can 9 students be selected and arranged in a row with 5 men in the middle and 2 women on each end?
Click here to see answer by Edwin McCravy(20054)

Question 942792: A dice is thrown three times and the sum of three numbers thrown is 15. Find the probability that the number on the first throw is 4.
Click here to see answer by Edwin McCravy(20054)

Question 943371: A theater has 48 seats arranged in 8 rows of 6 seats each. three friends buy tickets separately. what is probability they will end up in same row?
Click here to see answer by Edwin McCravy(20054)

Question 943370: a clerk distributes packages among 4 trucks. what is probability that three packages wind up in different trucks? What is probability if clerk is given 20 packages, that exactly five of them wind up on each truck?
Click here to see answer by Edwin McCravy(20054)

Question 943735: A husband has 7 relatives, 4 of them are
women and the rest men. His wife too
has 7 relatives out of which 3 are
women and 4 men.
In how many ways can they invite a
dinner party of 3 ladies and 3 men so
that there are 3 of man's relatives and
3 of wife's ?
Click here to see answer by Edwin McCravy(20054)

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