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

Tutors Answer Your Questions about Permutations (FREE)

Question 379058: is there 362880 distinguishable of the letters in the word TEXTBOOKS? explain.
Click here to see answer by richard1234(5390)

Question 379058: is there 362880 distinguishable of the letters in the word TEXTBOOKS? explain.
Click here to see answer by stanbon(57224)

Question 379247: Find the fifth term of (7x+2y)^15
This is what I have so far.
(n)
(r) (a)^n-r(b)^r
a=7
b=2
n=15
r=4
15 nCR 4*(7)^11*(2)^4
The answer that the calculator gives you is 4.32^13. I am confused about what exponents I put for x and y since the solution of the equation has an exponent involved with it. Any help would be appreciated. Thanks!
Click here to see answer by robertb(4012)

Question 379462: in how many ways can 6 different trees be planted in a circle

Click here to see answer by richard1234(5390)

Question 380103: how would a person prove the result algebraically of this problem nCr = nCn-r
and explain why it must be true using a Pascals Triangle.
Click here to see answer by richard1234(5390)

Question 380105: with out adding how would a person solve
at least 1 spade
directions: find the number of possible 5-card hands that contain the cards specified. The cards are taken from a standard 52-card deck.
Click here to see answer by richard1234(5390)

Question 380284: In how many ways can a group of four or more be form from ten people
Click here to see answer by richard1234(5390)

Question 380393: How many possible starting lineups of 5 players from a 12-man roster can you form?
Click here to see answer by richard1234(5390)

Question 382020: A group of 30 state representatives are on the state’s telecommunications committee; 20 of them are Democrats and 10 of them are Republicans. If a subcommittee of 8 members needs to be formed from the telecommunications committee, then answer the following: (Show how you arrived at your answer. Use the proper mathematical notation.)
How many different groups can be formed if there at most 6 Republicans on the subcommittee?
Click here to see answer by edjones(7569)

Question 382068: In how many ways can 4 people be assigned to seats in a 12-seat room? Show how you arrived at your answer.
Click here to see answer by user_dude2008(1861)

Question 382618: in how many ways can a committee of 4 men and 5 woman be formed from a group of seven men and seven woman?
Click here to see answer by robertb(4012)

Question 382715: how many 3 digit numbers can be formed is the leading digit cannot be 0?
Click here to see answer by richard1234(5390)

Question 382947: How many different four-letter words can be formed from the letters: a,b,c,d,e,f, and g if no repetition of letters is allowed ?
Click here to see answer by edjones(7569)

Question 382852: A group of 14 must select a president, a vice-president, a treasurer and a secretary. How many ways can this be done?
Click here to see answer by nyc_function(2733)

Question 383270: (2n+1)!/(n+2)! * (n-1)!/(2n-1)!=3/5 what is n?
Click here to see answer by stanbon(57224)

Question 383380: what is 15 girls out of 40 students
Click here to see answer by solver91311(16868)

Question 383445: In how many ways can 5 people be assigned to seats in a 9 seated room?
Click here to see answer by robertb(4012)

Question 383823: What is the sum of the numbers in row 5 of Pascal's triangle?
Click here to see answer by edjones(7569)

Question 383822: In a survey with 54 member, 20 were taking mathematics, 35 were taking English, and 6 were taking both. How many were not taking either subject?
Click here to see answer by edjones(7569)

Question 383821: In how many ways can a group of 11 elect a president, secretary, and treasurer?
Click here to see answer by edjones(7569)

Question 383824:
There are five girls and five boys at a party. In how many ways can they be seated in a row of six?
Click here to see answer by edjones(7569)

Question 383186: How many different ways can a gold, a silver, and a bronze medal be awarded to 6 runners?
Click here to see answer by sudhanshu_kmr(1152)

Question 385297: the digits 4,5,6,7,8,9 are randomly arranged to form a three-digit number. (digits are not repeated) find the probability that the number is even and greater than 900
Click here to see answer by sudhanshu_kmr(1152)

Question 385048: SEVEN HOUSES IN A ROW ARE TO BE PAINTED WITH ONE OF THE COLORS RED, BLUE, GREEN OR YELLOW. IN HOW MANY DIFFERENT WAYS CAN THE HOUSES BE PAINTED SO THAT NO TWO ADJACENT HOUSES ARE THE SAME COLOR?
Click here to see answer by sudhanshu_kmr(1152)

Question 385348: Ten fish are caught in a lake, marked, and then returned to the lake. Two days later 20 fish are again caught, 2 of which have been marked.
(a) Find the probability of 2 of the 20 fish being marked if the lake has k fish (assuming the fish are caught at random).
(b) What value of k maximizes the probability?

Click here to see answer by stanbon(57224)

Question 385347: What is the probability that 2 (or more) people in a random group of 25 people have a common birthday? (This is the famous Birthday Paradox Problem.)
Click here to see answer by sudhanshu_kmr(1152)

Question 385820: Allen is in the Boy Scouts. He has three weeks left in which to complete the hours required for a merit badge in community service. Because of his paper route and homework, he can't put in more than 5 hours in any one week for the merit badge. How many different ways can Allen work a total of 10 hours over the three week period? So far I have 23 different combinations. I am wondering if that is the total or if there is more.
Click here to see answer by scott8148(6628)

Question 386769: If nPr = 120, and nCr=20, then determine the value of 7Pr.
Click here to see answer by jim_thompson5910(28476)

Question 386769: If nPr = 120, and nCr=20, then determine the value of 7Pr.
Click here to see answer by solver91311(16868)

Question 386796: How many ways can 3 couples sit in a row in a movie theater if all couples must sit together?

Click here to see answer by robertb(4012)

Question 386772: If a term in the explansion of (x+b)^8 is (-1701x^3)/(4096), assuming b is a constant, then the exact value of b is?
Click here to see answer by robertb(4012)

Question 386793: Determine the no. of terms in the expansion (2x^2-(1/4x))^12.
I got 13, by using the binomial theorem. Is there a way that I don't need to expand till the end?
Click here to see answer by Fombitz(13828)

Question 386795: Little Lenny Leonardson has 2 red blocks, 3 blue blocks and 2 yellow blocks. in how many diff ways can he line up the blocks?
How do you know when to use permutation OR combinatorics?
Click here to see answer by sudhanshu_kmr(1152)

Question 386910: Please help us understand this Algebra homework. I do not believe the teacher really explained this in class, and my child is confused. Thank you so much.
1) How many different license plates can be made that contain 4 letters and 3 numbers if repeating is allowed, but you cannot use Q or 7?
2) Using the digits 2,4,6,7,8 only?
a) How many 4-digit numbers can be made if repeating is allowed?
b) How many 4-digit numbers can be made if no repeating is allowed?
c) If you can repeat numbers, how many 3-digit numbers are possible that are greater than 600?
d) if no repeating is allowed, how many 5-digit numbers can you make that are greater than 60,000 and also odd?

Click here to see answer by sudhanshu_kmr(1152)

Question 387020: the probability that both Barb and Bob are both on the same committee of 4 which is choosen from their class of 10 people is?
Click here to see answer by sudhanshu_kmr(1152)

Question 387019: the probability that both Barb and Bob are both on the same committee of 4 which is choosen from their class of 10 people is?
Click here to see answer by robertb(4012)

Question 387269: How many different ways can a committee of 9 be
selected from a larger organization of 20 people?
Click here to see answer by robertb(4012)

Question 387292: suppose a code is made up of three numbers followed by 2 letters if the number 0 or 1 may not used at the beginning of the code how many codes are possible
Click here to see answer by edjones(7569)

Question 387810: A ten-person club must select a president, a vice-president and a secretary treasurer. They must also select a 3 person committee. If the officers may not serve on the committee, in how many ways may both selections be made?
Assume one person cannot be assigned more than one position.
Click here to see answer by stanbon(57224)

Question 388015: i want some very difficult questions in permutations and Combinations with the solutions and explanations >>> please
Click here to see answer by mdenny(8)

Question 388090: There are 6 boys and 4 girls and a group of 5 people must be formed. How many groups are possible consisting of 2 girls and 3 boys?
Click here to see answer by edjones(7569)

Question 388089: You toss a fair 6-sided die 5 times.find the probability that a three is rolled exactly two out of the five rolls.

Click here to see answer by ewatrrr(10682)

Question 388086: You toss a fair 6-sided die 5 times. Find the probability that a three is never rolled.
Click here to see answer by ewatrrr(10682)

Question 388086: You toss a fair 6-sided die 5 times. Find the probability that a three is never rolled.
Click here to see answer by solver91311(16868)

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