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

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Question 142571: How many 5-card hands having exactly 3 aces and 2 other cards can be dealt?
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Question 142570: How many 13-card hands having exactly 11 diamonds can be dealt?
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Question 142569: A school club has 15 boys and 16 girls as members. How many different 6- person communities can be selected from the membership if equal numbers of boys and girls are to be selected?
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Question 143259: Make an organized list of all possible four-letter permutations of the letters in STEP?
I know by calculating that it should be 4*3*2*1=24 - however I only come up with STEP, TEPS, PSTE, EPST - how do I find all 24 words?
Thanks
Click here to see answer by solver91311(24713)

Question 143285: A committee for the end-of-year party is composed of four eighth graders and three seventh graders. A three-member subcommittee is formed...
Find the probability that all 3 members on the subcommittee are eighth graders?
Thanks for your help
Click here to see answer by stanbon(75887)

Question 143281: Charmayne is organizing a track meet. There are 4 runners in her class. Each runner must compete one-on-one against each of the other runners in her class.
How many races must Charmayne schedule? This would be 4*3*2*1=24 (Is this correct?)
Must Charmayne schedule permutations or combinations? Permutations (Is this correct?)
Thanks
Click here to see answer by stanbon(75887)

Question 143306: Abe, Brian, and Carmela share the responsibility of caring for the family pets. During a seven-day week, Abe and Brian each take three days and Carmela the other one. In how many different orders can the days of a week be assigned?
I'm not sure but i did this:
7!/(3!*3!*1!) and the answer I got is 140 different ways. Is this right?
Click here to see answer by stanbon(75887)

Question 143575: Cassandra has six different colored bracelets. In how many ways can she wear three bracelets at a time?
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Question 143572: Please help me sovle this extended word problem:
Cassandra has three skirts, five blouses, and ten pair of shoes, how many outfits does this make?
Click here to see answer by MathTutorer(13)

Question 143571: Please help me solve this extended word problem:
Given the following crcumstances tell if a combination or permutation and solve.
a. Cassandra has seven skirts, five blouses, and ten pair of shoes, how many outfits can she create?
Click here to see answer by vleith(2983)

Question 143578: Give three other names for a root and describe the connection to the graph of the polynomial.
Click here to see answer by nabla(475)

Question 143959: A standard license plate has six spaces for either numbers or letters to be engraved:
If you are allowed to use numbers OR letters in each slot, how many different license plates are possible to make (repeating allowed)?
How does this number change if you were restricted to the following constraint:
The first three slots can only be letters, and the second three slots can only be numbers (you can repeat).
Click here to see answer by vleith(2983)

Question 144493: A shipment of ten television sets contains 3 defective sets. How many ways can a hospital purchase 4 of these sets and recieves at least 2 of the defective sets?
Click here to see answer by josmiceli(19441)

Question 144550: I am stuck on this combination / Permutation problem. I was hoping someone could please help me.
The company in problem 8 wants to streamline the selection process by limiting the number of choices to just one file cabinet or one bookcase. (The employee will still choose one or the other.) How many different configurations can be created in this new situation?
Thanks so much ~Lyn
Click here to see answer by solver91311(24713)

Question 144794: How many ways can 4 people be chosen from a group of 9? Tell wheater the situation is permutation or combination
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Question 145160:
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Question 146045: What is the difference between a Permutation and a Combination?

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Question 146044: I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected?

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Question 146043: I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls?

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Question 146042: State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery?

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Question 146036: Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
How many different two-digit numbers can be formed from the digits 3, 1, 4, and 5 (allowing reuse)?

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Question 146032: Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
In how many different ways can you arrange the letters of the word INTERNET?

Click here to see answer by BrittanyM(80)

Question 146034: Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
In how many different ways can you arrange the letters of the word TRIGONOMETRY?

Click here to see answer by BrittanyM(80)

Question 146039: Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
The Board of Directors does not have assigned seats in the conference room. If there are 12 of them, seated at a round table, how many different seating arrangements are possible?

Click here to see answer by BrittanyM(80)

Question 146041: A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses.
How many ways can 4 toppings be selected where:
a.) All the toppings are vegetables
b.) All the toppings are meat
c.) There is only cheese on the pizza
d.) There are 2 vegetables, 1 meat and 1 cheese
e.) There are 3 meats and 1 cheese.
What's your favorite combo?

Click here to see answer by edjones(8007)

Question 146040: Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if:
a.) the first letter must be Y
b.) the vowels and consonants alternate, beginning with a consonant (Y is a consonant here and Y does not have to be first).

Click here to see answer by stanbon(75887)

Question 146037: Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
Of 10 candidates, the first 6 are being interviewed in the morning, and the last 4 in the afternoon. In how many ways can the interviewer arrange a schedule?

Click here to see answer by oscargut(2103)

Question 146038: Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
How many seven-digit phone numbers can be formed if the first digit cannot be 0 and
a.) repetition of digits is not permitted?
b.) if repetition of digits is permitted?

Click here to see answer by oscargut(2103)

Question 146035: Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
In how many different ways can the 9 starters of a baseball team be placed in their positions?

Click here to see answer by edjones(8007)

Question 146033: Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
In how many different ways can you arrange the letters of the word COMPUTER taking 4 at a time?

Click here to see answer by edjones(8007)

Question 146031: Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
In how many different ways can 6 classes be scheduled during a 6-period day?

Click here to see answer by checkley77(12844)

Question 146985: The Binomial Theorem...When (2a + b)^8 is expanded, what is the coefficient of the term a^3b^5? A little rusty but this is what I have done so far
the binomial coefficient is 8 over 5...evaluated would be 8!/3!*5!=56
then 56(2^3)(1^5)=448 I'm not sure that I did this correctly.
Thanks

Click here to see answer by scott8148(6628)

Question 147594: Jasmine says that there are 362,880 distinguishable permutations of the letters in the word TEXTBOOKS. Do you agree? Justify your answer.

Click here to see answer by stanbon(75887)

Question 147612: How many different auto tags can be made by 3 letters followed by 3 numbers if no repitition is permitted? Both the letter o and the number 0 are allowed.
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Question 147870: The problem is P(n,2)=42, find n. The instructor gave the answer for n, which is 7. I figured out the formula knowing the answer is 7, which is n!/(n-k)!
I need to know the formula to figure out how to get the value of n. Thank you.
Click here to see answer by stanbon(75887)

Question 148291: How many ways can a baseball coach choose the first, second and third batters in the lineup of a team of 15 players.
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Question 148292: On a bench that seats five people, how many ways can five people be seated?
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Question 148292: On a bench that seats five people, how many ways can five people be seated?
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Question 148289: If a license plate does not contain any vowels (A, E, I, O, U) or the number 5. How many different possibilities outcomes for the license plate?

Click here to see answer by Alan3354(69443)

Question 148347: suppose there are ten items on a true false test the person taking the test does not read the questions but answers randomly what is the probability of him answering all 10 qestions correctly aolve using permutations
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Question 149135: What two intergers can you multiply not using zeros to equal one million?
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Question 149385: find the number of ways a sandwich can be make from choosing 1 each of the following: white or wheat bread, and turkey, ham, or roast beef, and american cheese, swiss cheese, or cheddar cheese, and mayo or mustard.
I am confused as to which # (n,r) are
Click here to see answer by scott8148(6628)

Question 149387: From a club of 25 members, how many ways can a president, vice-president, secretary, and treasurer be selected?
which formula is used and does n=25 and r=4?
Click here to see answer by jim_thompson5910(35256)

Question 151266: There ia a question paper consisting of 10 questions. Each question has interval choice of 2 questions. in how many ways can a student attempt one or more question of the given ten question of the paper.
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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