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

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Question 599207: An internet site requires a 6 character password made up of 2 digits followed by 4 letters where uppercase letters are not the same as lowercase letters. Without repetition of letters or numbers, how many different passwords can be created?
Click here to see answer by math-vortex(472)

Question 599323: You volunteer to help drive children at a charity event to the zoo, but you can fit only 7 of the 17 children present in your van. How many different groups of 7 children can you drive?
Click here to see answer by jim_thompson5910(28595)

Question 599396: If you can answer any 12 questions from total of 15 questions, how many different ways can you select the questions?

Click here to see answer by jim_thompson5910(28595)

Question 599401: There are three couples who are attending a movie. If the two members of each couple wish to sit together during the movie, how many ways can the couples be seated?

Click here to see answer by edjones(7569)

Question 600069: A clerk had only 10 vacant rooms left in one hotel. There were 11 men who went into the hotel at the same time, each wanting a separate room. The clerk, settling the argument said, "I'll tell you what I'll do. I will put two men in Room 1 with the understanding that I will come back and get one of them a few minutes later." The men agreed to this. The clerk continued, "I will put the rest of you men as follows:
the 3rd man in Room 2
the 4th man in Room 3
the 5th man in Room 4
the 6th man in Room 5
the 7th man in Room 6
the 8th man in Room 7
the 9th man in Room 8 and
the 10th man in Room 9
Then the clerk went back to get the extra man he had left in Room 1, and put him in Room 10. Everybody is happy. What is the fallacy of this plan?
Click here to see answer by htmentor(789)

Question 600532: A basketball team consists of 11 players. In how many ways can a coach choose the five starting players, position of the player not being considered
Click here to see answer by jim_thompson5910(28595)

Question 600714: Find the number of ways in which each commitee can be selected.
-3 people from a group of 5
Click here to see answer by jim_thompson5910(28595)

Question 601074: How many ways can you rearrange 12 eggs ? Do you use 12! Or permutations ?
Click here to see answer by solver91311(16897)

Question 601074: How many ways can you rearrange 12 eggs ? Do you use 12! Or permutations ?
Click here to see answer by Edwin McCravy(8909)

Question 601151: In how many ways can the names of eight candidates for political office be listed on a ballot?
Click here to see answer by solver91311(16897)

Question 601640: the total number of ways in which six 't' and four '-' signs can be arranged in a line such that no two '-' signs occur together is?
Click here to see answer by Edwin McCravy(8909)

Question 601734: Please help me solve this problem: How many 4-letter code symbols can be formed with the letters P,D,Q,X without repetition?
Click here to see answer by jim_thompson5910(28595)

Question 601739: Whats the formula and answer for this problem:
A women is going out for the evening.She will put on one of 6 dresses, one pair out of 8 pairs of shoes, and go to one of 7 restaurants. In how many days can this be done?
Thank You in advance!
Click here to see answer by josmiceli(9690)

Question 601827: A computer password consists of a letter of the alphabet followed by 3 or 4
digits. Find the total number of –
(a) passwords that can be formed
(b) passwords in which no digit repeats
Click here to see answer by Jacksonjacob(3)

Question 602036: Four cards labeled A, B, C, and D are randomly placed in four boxes labeled A, B, C, and D. Each box receives exactly one card.

Click here to see answer by richard1234(5390)

Question 602332: Help please on Permutations.
Problem:
how many ways can 15 students be separated into two groups of 8 and 7?
Attempt:
Since they will be separated into 2 groups, i tried using 15!/7! since the rest (those seven left) will be on the other group, but it does not show the combinations for the other group. And so i am wrong. :/
Click here to see answer by scott8148(6628)

Question 602377: How many different ways can you arrange the letters A,B,C, and D?
Click here to see answer by jim_thompson5910(28595)

Question 602504: if you have 3 chairs and 5 people how many different arrangements can you come up with?

Click here to see answer by jim_thompson5910(28595)

Question 602845: A multiple-choice quiz consists of 5 questions, each permitting a choice of 3
alternatives. In how many ways may a student fill in the answers if they answer
each question?
Click here to see answer by flame8855(424)

Question 604095: The door code to get into a top secret laboratory is 6 digits. the first 3 digits of the code are all odd and the last 3 digits are all even. Digits can be used more than once. How many possible codes are there to gain access to this laboratory?
This is a Permutations and Combinations question.
Click here to see answer by jim_thompson5910(28595)

Question 604146: How many ways can you make a sandwich by choosing 4 of 10 ingredients
Click here to see answer by Edwin McCravy(8909)

Question 604459: How many five card hands consisting of 3 kings and 2 aces can be dealt from a deck of 52 playing cards?
Click here to see answer by stanbon(57377)

Question 604518: Janet sits on the 7th chair from each end of a row. How many chairs are there in a row?
Click here to see answer by solver91311(16897)

Question 604594: How many 4-element subsets containing the letter A can be formed from the set {A,B,C,D,E,F,G}?
Click here to see answer by Edwin McCravy(8909)

Question 604720: Hi, I have a math problem that almost no one in my class can solve:
How many multiples of 3 between 100 and 1000 can be formed from the digits 1, 4, 5, 6, and 8?
Please answer, and thanks!
Click here to see answer by scott8148(6628)

Question 604761: The number of ways in which 12 students can be equally divided into three groups is
Click here to see answer by AnlytcPhil(1277)

Question 604829: How many signals can be formed from 4 flags of different colors using all at a time?
Click here to see answer by stanbon(57377)

Question 604776: In how many ways can 3 people be selected from 20 candidates?
for some reason I did 3 x 20 and get 60 but feel wrong.
Click here to see answer by lawdej(58)

Question 604911: Jace's collection of sports cards includes ten baseball, seven basketball, and nine football cards. He wants to give away two cards from different sports to his friend for a birthday present. How many ways can he choose the two cards?
I have tried 26P2 and 26C2 but I am not sure if any of these are right. I have also tried 26!/10!7!9!
I am not sure if I am working this problem out right. Please help my understand how this problem is worked out.
Thank you so much for your help!
Click here to see answer by jim_thompson5910(28595)

Question 604615: A commitee of 9 is to be selected from 6 women and 8 men.in how many ways can this be done if the committee must contain at least 4 women?
Click here to see answer by scott8148(6628)

Question 604708: There are 10 first-tier national rugby union teams.
(a) How many different two-team pairings are possible among those 10 teams.
I guess, the answer to this will be C(10,2) = 45 ways
I am stuck in the following
(b) how many different ways are there to select a 1st, 2nd and 3rd ranked teams from these teams
(c) Suppose 4 teams are going to gather in Sydney, the other 6 teams in Melbourne. How many ways it can be done?
Thanks

Click here to see answer by scott8148(6628)

Question 605243: 6 boys and 5 girls are to be seated around a table. Find the number of ways that this can be done in each of the following cases.
a. there are no restrictions
b. no 2 girls are adjacent
c. all girls form a single block
d. a particular girl G is adjacent to two particular B1 and B2
Click here to see answer by Edwin McCravy(8909)

Question 605367: How many can combinations can someone make with 8 shirts and 6 pants

Click here to see answer by jim_thompson5910(28595)

Question 605823: You are given the following seven-digit number: 4064465.
How many different seven-digit numbers can be made by rearranging the digits of 4064465?
Click here to see answer by Edwin McCravy(8909)

Question 605873: If no digit appears more than once, how many 5-digit numbers can be formed from the digits 2, 3, 4, 6, and 7?
Click here to see answer by jim_thompson5910(28595)

Question 606185: tell me about basic of permutation
Click here to see answer by mathie123(224)

Question 606393: nP6=6(nP4)
so far I have: n!/(n-6)!=6[n!/(n-4)!]
Click here to see answer by scott8148(6628)

Question 606525: how many different three letter codes are there if only the letters a,b,c,d,e,f are used and no letter is used more than once?

Click here to see answer by stanbon(57377)

Question 606896: what is the combination? ( choose 4 people from 6 )
Click here to see answer by solver91311(16897)

Question 607029: So there are three seats, each one can either be filled by a boy or a girl. How many different combinations are there with repetition?
I know that there are 4:
BBB
BBG
BGG
GGG
However, I don't know the equation to find this... Could you help? Much obliged!
Click here to see answer by jim_thompson5910(28595)

Question 607044:
Click here to see answer by sophxmai(60)

Question 607052: a 40 row theater has 10 seats in the front row. the second row has 11 seats. if each row has one more than the row in front of it how many seats are there in the theater
Click here to see answer by josmiceli(9690)

Question 607088: in how many ways can 8 students be seated in a row of seats to take an exam?
Click here to see answer by lynnlo(4164)

Question 607027: If 7 students are at a bus stop, how many ways can they enter the bus when it arrives?
Click here to see answer by lynnlo(4164)

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