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

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Question 632221: Find the number of 7 digit phone numbers that can be formed if the first three digits come from the numbers 1 to 3 and the last four digits come from the numbers 1 to 9
Click here to see answer by graphmatics(170)

Question 632277: at a local resaturant a new dinner menu is available that offers 4 courses an appetizer a salad a main dish and a dessert all for one price there are 7 appetizers 2 salads 4 main dishes and 4 desserts how many dinner outcomes are possible
Click here to see answer by rapaljer(4667)

Question 632578: A student taking an examination is required to answer exactly 10 out of 15 questions.

a. In how many ways can the 10 questions be selected?
b. In how many ways can the 10 questions be selected if exactly 2 of the first 3 questions must be answered?

Click here to see answer by reviewermath(602)

Question 632814: how many even numbers of four different digits each can be formed from the digits 3,5,6,7,9
Click here to see answer by josmiceli(9817)

Question 632886: In how many ways can 3 boys and 5 girls be arranged in a row so that all the 3 boys are together
Click here to see answer by ewatrrr(10682)

Question 632962: In how many ways can five couples be seated in a row of 10 chairs if no couple is seperated?
Click here to see answer by stanbon(57966)

Question 633024: an ice cream store sells 23 flavors of ice cream, determine the number of 4 dip sundaes. how many are possible if order is not considered and no flavor is repeated?
Click here to see answer by graphmatics(170)

Question 633398: how many ways can we arrange four girls and three boys in a row if the girls are to seat side by side?
Click here to see answer by ewatrrr(10682)

Question 633397: how many ways can we arrange four girls and three boys in a row if the girls are to seat side by side?
Click here to see answer by ewatrrr(10682)

Question 633541: Assume a class has 26 members. How many committees of 12 can be chosen?
Click here to see answer by Edwin McCravy(8999)

Question 633751: MicroCorp will hold its annual company picnic next week and will assign 3 planning duties to its employees.One person selected will reserve a venue,another will arrange catering,and a third will plan activities.There are 10 employees eligible to fulfill these duties,and no employees can be assigned more than one duty.How many different ways are there for duties to be assigned to employees?
Click here to see answer by jsmallt9(3296)

Question 634032: How many 6 digit numbers can be made from 2 different digits (e.g. 3 and 7 = 333777, 373737 etc).
Also, is there a simple way to work this out?
Thank you
Caitlan Smith
Click here to see answer by Alan3354(31518)

Question 634493: how many 4 person committes can be made wih 18 people
Click here to see answer by stanbon(57966)

Question 634501: pls show how is (n)!.(n+2)=(n)!+(n+1)!
Click here to see answer by stanbon(57966)

Question 634714: There are 17 common first names, 130 common middle names, and 193 common last names. How many unique character names can be generated?
I thought I should multiply the three numbers; however, I am confused because of the word unique.
Character names are first name, middle name, and then last name.
Thank you in advance for any assistance you may provide.
Click here to see answer by stanbon(57966)

Question 634811: Find the number of ways in which nine books can be arranged in a shelf if four particular books are to be kept together.
Click here to see answer by ewatrrr(10682)

Question 634814: In the game of “craps” two fair dice are rolled. If the total of the faces equals 7 or 11, you win. If the total is 2, 3, or 12, you have thrown craps and you lose. In all other cases, you throw again.
a. How many possible outcomes for that event of wining?
b. How many possible outcomes for that event of losing?
c. How many possible outcomes for that event of needing to throw again?

Click here to see answer by ewatrrr(10682)

Question 634812: Find the number of ways by which a president’s wife can invite at least two from 8 cabinet members’ wives to a tea party.
Click here to see answer by ewatrrr(10682)

Question 634813: How many three digit even numbers less than 500 can be formed from the integers 1, 2, 3, 4, 5, 6, and 7 if the integers cannot be used more than once?
Click here to see answer by jim_thompson5910(28715)

Question 635094: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Click here to see answer by ewatrrr(10682)

Question 635133: How many phone numbers are there with the code 270?
Click here to see answer by jim_thompson5910(28715)

Question 636148: a computer randomly generates a four letter password. how many passwords are possible if letters may repeat?
Click here to see answer by jim_thompson5910(28715)

Question 636147: in a crowd of ninety people, how many ways can ten digital music players be given away?

Click here to see answer by jim_thompson5910(28715)

Question 636149: (1 pt) (a) A particular brand of shirt comes in 13 colors, has a male version and a female version, and comes in 4 sizes for each sex. How many different types of this shirt are made?
Click here to see answer by jim_thompson5910(28715)

Question 636252:
Click here to see answer by jim_thompson5910(28715)

Question 636253: What is the Five digIt nUmber we can make using the digits
5,4,0,8 ?

Click here to see answer by ewatrrr(10682)

Question 636382: A travel app will suggest 3 hotels and 5 restaurants at random for any city it has information. How many different suggestions can it make for a town that only has 8 hotels and 18 restaurants?
My thinking is C(8,3) + C(18,5). Am I on the right track?
Thank you in advance for any assistance.
Click here to see answer by solver91311(17077)

Question 636501: in a poker game how many ways can you form a full house

Click here to see answer by Alan3354(31518)

Question 636582: How many 3-digits numbers can be formed from the digits 0,1,2,3,4,5 and 6 if each digit can be used only once.
Click here to see answer by stanbon(57966)

Question 636760: 18Cr=18C(r+2). what is the value of rC5?
Click here to see answer by sachi(454)

Question 636761: nC(r-1)=56
nCr=28
nC(r+1)=8
what is the value of r?
Click here to see answer by ewatrrr(10682)

Question 636766: (n1+n2)P2=132
(n1-n2)P2=30
then n1 & n2 is?
Click here to see answer by ewatrrr(10682)

Question 636931: A particular level of a tower defense game requires you to place 10 towers that enemies will attempt to pass in order. There are 3 red towers, 5 grey towers, and 2 green towers to choose from for this level. How many different arrangements of towers are possible?
My thinking is 3! * 5! * 2! Am I on the right track?
Thank you in advance for any assistance.
Click here to see answer by stanbon(57966)

Question 637017: A student is asked to answer 8 out of 14 questions on an exam. In how many ways can she select the question to be answer
Click here to see answer by ewatrrr(10682)

Question 637143: how many words are there in d alfabet A-Z. Using numeric answer
Click here to see answer by solver91311(17077)

Question 637329: On a shelf of 24 books how many combinations of arrangement are possible
Click here to see answer by ewatrrr(10682)

Question 637616: How many different comittees can be chosen from 8 female and 10 male club members, if each committee is to contain 3 females and 3 males?
If you could explain the steps involved to calculating this it would be much appreciated!
Thanks,
Dom.
Click here to see answer by god2012(108)

Question 637650: A typical Social Security number is 555-47-5593. How many Social Security numbers are possible if the first two digits cannot be 0?
Click here to see answer by MathLover1(6812)

Question 637853: I know how to set the problem up but I do not understand how they the get the answer to this problem:
How many ways can seven books be arranged on a book shelf?
The answer is: 7!/1=5,040
Click here to see answer by stanbon(57966)

Question 638033: Mr. and Mrs. Richardson want to name their new daughter so that her initials (first, middle, and last) will be in alphabetical order with no repeated initial. How many such triples of initials can occur under these circumstances?
Click here to see answer by Theo(3504)

Question 638494: A lumberjack has 4n + 110 logs in a pile consisting of n layers. Each layer has two more logs than the layer directly above it. If the top layer has six logs, how many layers are there?
Click here to see answer by josmiceli(9817)

Question 638503: A class has 12 students. How many ways can a president and vice president be chosen?

Click here to see answer by checkley79(3056)

Question 638564: how many ways can the five starting positions on a basketball team be filled with nine who can play any of the positions?
Click here to see answer by stanbon(57966)

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