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

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Question 959748: A menu at a restaurant offers 9 different appetizers. How many different ways can a group choose 4 appetizers?
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Question 959789: The 16 members of a soccer team are travelling to a match in 3 vehicles, which have room for 7, 5 and 4 passengers, respectively. In how many ways can the team be seated in the vehicles?
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Question 959838: please help me explain why 0! is equal to 1.thanks in advance
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Question 959540: a four digit code is created from the digits 0 to 9. how many of these codes can be created if 0 cannot be the first digit, no digit may be repeated, and the last digit must be 5

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Question 960030: In a hotel in Hong Kong, a room key is a card. The card has positions for holes that form a 4 by 6 arrays. Each position in the array is either punched with a hole or left blank. How many different keys are possible?
The answer is 16777216, but I am not sure what are the steps to solving this.

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Question 960035: A president, vice president, secretary, and treasurer are to be chosen from among 8 people.Anna, Ben, Clare, Derek, Eric, Jessica, Michael and Martin. No person can hold more than one office and the treasurer must be a woman. Determine the number of ways the office can be filled. The answer is 630, but I was looking for the steps to solve this problem.
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Question 960174: What numbers come from 1147
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Question 960167: solve detail:
Q) what are the possible arrangement of 6 student in one bench if younger sit at left?

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Question 960370: how to find the total number of 9- digit numbers having all different digits
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Question 960346: You download 15 music files on your computer and plan to save 7 of them to an mp3 player. In how many ways can u arrange the songs. I need to know how many ways anfd if it is a Combination or a Permutation

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Question 960431: 9 students try out for 3 openings on the school soccer team. How many ways can 3 students be chosen out of 9?
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Question 960409: A bookshelf has space for 8 books. If 13 books are available, how many different arrangements can be made on the shelf?
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Question 960531: Find n. nP4=3(nP3) (Linear Permutations)
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Question 960648: There were 20 girls and 30 boys in the second session. What is the percentage of boys in the second session of swimming lessons
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Question 960569: What is the highest power of 15 in the expansion in 30!thanks in advance.
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Question 960688: Jeanie baker makes flower arrangements. There are 11 different cut flowers and she plans to use 6 of them. How many different selections of the 6 used are possible
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Question 960740: there are 5 girls and 5 boys in a tennis team. How many ways can one 'mixed doubles' pair be selected

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Question 960839: An appliance delivery person has 5 deliveries to make. The destinations are all so close, it doesn't matter the order in which the appliances are delivered. In how many orders can the deliveries be made?
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Question 960839: An appliance delivery person has 5 deliveries to make. The destinations are all so close, it doesn't matter the order in which the appliances are delivered. In how many orders can the deliveries be made?
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Question 960836: Seven friends go to a concert. In how many different ways can they sit together in a row of 7 empty seats?
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Question 960965: The instructions say "indicate whether each situation involves a combination or permutation. Then solve." I'm having trouble telling which is which. The first one is "how many ways are there to select five actors from a troupe of nine to improvise a scene?" Once I know which it is, I'll be able to solve it, but I can't tell whether it's a combination or permutation. Thanks!!
Click here to see answer by mathluva(1) About Me 

Question 960568: How many zeroes at the end of 25!pls help with explanation.thanks in advance
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Question 960975: there are 10 teams competing in the national math competition if only the first four teams are awarded medals how many possible arrangments of first second third and fourth are possible
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Question 961428: In how many ways can 9 people be seated on a bench if only 3 places are available?

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Question 961540: A committee of four is to be selected from a group of sixteen people. How many different committees are possible, given the following conditions?
a) One person is the chair, and the rest are general members?
b) One person is the chair, one person is the secretary, one person is responsible for refreshments, and one person cleans up after meetings.

How many five card poker hands consisting of all hearts are possible?
How many five card poker hands consisting of all cards of the same suit are possible?

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Question 961615: in how many different orders can 12 songs on a CD be played?
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Question 946844:
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Question 946844:
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Question 961668: How many distincts permutation can be made from the letters of the word COLUMNS?
How many of these permutations start with the letter M?

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Question 961986: 1,3,5,7,9,11,13,15 use this alphabet and three blanks total 30 how its possible
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Question 962070: How many number sequences can you get using only the numbers from 1 through 9 and that is only 6 digits long?


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Question 962105: How many ways can a soccer team choose its captain and its assistant captain with a team of 22 players?
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Question 962246: The sum of 3 odd numbers between 1 to 15 is equal to 30 ..will it come?
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Question 962286: an entertainment company must select 10 0f 19 possible entertainers for its summer schedule. In how many ways can be this be done?
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Question 962320: How many four letter passwords can be formed from the letters in the word panicky if letters are allowed to be repeated?
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Question 962401: there are four bus lines between a and b and 3 lines between b and c. find the number of ways that a man can travel by bus roundtrip from a to c by way of b

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Question 962523: An office building has 7 doors. Four doors are only entrances to the building and two doors are only exits from the building. In how many different ways can someone enter and exit the building?
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Question 962557: a group of five children has to be chosen from a form of eight boys and twelve girls.in how many ways can the selection be made if the group must contain at least two boys and two girls?
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Question 962757: How many arrangements are there of the word MATHEMATICS?
How many of these start with the letter M?
How many of the arrangements in part a have the T’s together?

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Question 962649: There are 22 students on the debate team. The number of boys is two more than three times the number of girls. How many boys are on the team?
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Question 963114: 32C4. need help solving this.

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Question 963372: how many ways can you arrange nine pairs of shoes if they are not separated

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Question 963371: how many ways can you arrange nine pairs of shoes if they are not separated

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Question 963423: In a classroom, the same 5 students sit in the first row everyday, and the same 4 students sit in the second row everyday. Each row contains a total of 8 seats. How many different seating arrangements would there be in total if the students were to change their seats in their respective rows daily?
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Question 963454: how to find the answer in the three blanks if the numbers are in odd 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