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

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Question 213277: Out of 52 deck of cards, 4 cards are pulled out. What is the probability for:
a) all the cards to have the same value
b)all the cards to have the same sign
c) all the card to be in hearts

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Question 213282: it would be greatly appreciated if someone helped with the steps on this one..
the answer for a) is 95 040 and the answer for b) is 7920
Twelve different portraits are in the Ling family's collection
a) In how many ways could five of them be hung in a row on the living room wall?
b)If Grandma Ling's picture must be included and must be hung in the middle of the group of five, how many different arrangements are there?

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Question 213282: it would be greatly appreciated if someone helped with the steps on this one..
the answer for a) is 95 040 and the answer for b) is 7920
Twelve different portraits are in the Ling family's collection
a) In how many ways could five of them be hung in a row on the living room wall?
b)If Grandma Ling's picture must be included and must be hung in the middle of the group of five, how many different arrangements are there?

Click here to see answer by josmiceli(19441) About Me 

Question 213492: Can you give me a formula to work out the amount of squares within a square eg. a chess board
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Question 213492: Can you give me a formula to work out the amount of squares within a square eg. a chess board
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Question 213492: Can you give me a formula to work out the amount of squares within a square eg. a chess board
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Question 213847: I am trying to figure out how to set up the problem if a multiple choice test consists of 15 questions, each permitting a choice of three alternatives, in how many different ways can a student check these answers off?
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Question 214346: can you help me with this problem sirs.Thank you..
1.) For a national day parade display, 80 girls formed a large circle.The girls were equally spaced out and numbered in a clockwise direction from 1 to 80 by wearing a number tag.If Rose had tag no. 55,what was the number of the girl directly opposite to her?If Nina had tag no. 9,what was the number of the girl directly opposite to her?

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Question 214345: can you help me solve this problem sir....
1.) In order to encourage his son to study mathematics, a father agrees to pay his boy 50 centavos for every problem correctly solved, and to fine him 25 centavos for each incorrect solution.At the end of 30 problems neither owed anything to the other.How many did the boy solved correctly?


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Question 214344: can you help me solve this problem sir....
1.) In order to encourage his son to study mathematics, a father agrees to pay his boy 50 centavos for every problem correctly solved, and to fine him 25 centavos for each incorrect solution.At the end of 30 problems neither owed anything to the other.How many did the boy solved correctly?


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Question 214341: the total no. of 9 digit numbers of different digits is?
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Question 214956: Two machines make identical parts which are combined on a production
line. The older machine makes 40% of the units, of which 85% are of
satisfactory quality. The newer machine makes 60% of the units, of which
92% are satisfactory. A random check further down the production line
shows an unusual fault which suggests the machine which made the unit
needs some adjustment. Which machine is more likely to have made the
unit?

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Question 214954: In a lottery game the six winning numbers are chosen at random from
the set f {1,2,3 ..... 36}. Your entry consists of a similar choice. Find the
probability of:
(a) a win (i.e. your entry matches the winning numbers)
(b) a match four (i.e. exactly four of your entries have been chosen as
winning numbers)

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Question 214953: Five counters are selected at random from an urn which contains ten white
and forty black counters. Find the probability that exactly two of the se-
lected counters are white if the selections are made: (i) without replace-
ment; (ii) with replacement.
In case (i) fnd the probability that at least two of the selected counters
are white.

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Question 215180: How many permutations are there of 1,2,...,2n have every even number in an even-numbered position?
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Question 215552:
A committee of 5 people is to be selected from 6 women and 7 men. Find the probability that
a) all committee members are men.
How would you work this problem?

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Question 215776: how many distinguishable ways can the letters of the word VERTICAL be arranged using only 4 of the letters at a time?
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Question 216926: A mathematics class consist of 15 boys and 25 girls. A.In how many ways can the position of President, Vise-President, secretary, treasurer, and auditor be filled if no student may hold more than one position? B.In how many ways can 5 representatives be chosen from the class? C.If exactly 2 girls are chosen, in how many ways can the 5 representatives be chosen?
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Question 217296: Kindly answer this question please!!! Thanks!!! A housing contractor will build a house with 2,3, or 4 bedrooms, 1,or 2 bathrooms and a single garage. How many choices does he offer?
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Question 217296: Kindly answer this question please!!! Thanks!!! A housing contractor will build a house with 2,3, or 4 bedrooms, 1,or 2 bathrooms and a single garage. How many choices does he offer?
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Question 217319: In how many ways can 8 books be distributed to Mario and Luz, if Mario gets 5 books and Luz 3?
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Question 217314: 1.How many different signal can be made from 6 flags of which 3 are white, 2 are red and 1 is blue, if each signal consist of 6 flags placed one above the other?
2.How many different signal can be made from 5 different flags. If a signal consist of 5 flags placed one above the other on a flagpole?

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Question 217304: Kindly answer this question please!!! Thanks!!!! A commander pilot and an assistant for a flight to Mars are chosen from 15 astronauts. In how many ways can the two men be chosen for the 2 positions?
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Question 217297: kindly answer this question please!!! Thanks!!! Four numbers are to be formed from the digits 1,2,3,4,5,6,7 with no repetition allowed A.How many are less than 5000? B.How many are greater than 6000?
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Question 217312: Kindly answer this question please!!! Thanks!!! A gold, a silver, and a bronze medal are to be awarded to any 3 of the 12 contestant. In how many ways can the medals be given if A.anyone can be a winner B.The gold medal is to be awarded to a particular person?
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Question 217027: A sales man has 8 articles to display. In how many ways can he arrange his article?
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Question 217180: three men and three women line up at a checkout counter. In how many ways can they line up?
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Question 217738: 1. A club consist of 20 members. In how many ways can a committee of 4 be selected?
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Question 217737: 1. In how many ways can 5 questions be selected out of 8 questions?
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Question 218178: Kindly answer this question!!! Please!!! A car manufacturer offers 4 choices of body design, 10 color combination, and 3 different engines. How many different cars are required for a complete display?
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Question 218176: Kindly answer this question please!!! Thanks!! In how many ways 4 people be seated in a row of 6 chairs if A.they can be seated anywhere B. the empty chairs are adjacent to each other?
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Question 219118: if a train consists of four train cars how many times can it be arranged differently?
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Question 220704: Hi, i need help with this question!
A group consists of 5 democrats, 6 republicans, and 4 independents. Two group members are randomly selected in succession. Find the probability of selecting an Independent and then a democrat.
This is what I got so far...
# of democrats= 5, # of republicans= 6, # of independents = 4 TOTAL = 15 members
probability of selecting Independent 15C4/15
probability of selecting Democrat 15C5/15
** this is where i need help, i dont know where to go from here!

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Question 220699: 2!+(4!)(3!)
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Question 220713: HI!! i need help with this question..
You draw one card 52-card deck. The card is replaced and the deck and the deck is reshuffled, then you draw a second card. Find the probability of drawing jack the first time and a club the second time.
thank you for your help!!!

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Question 220739: A game is played using one die. If the dir is rolled and shows 1, the player wins $1. If the die is rolled and shows 2, the player wins $2, if the die is rolled and shows 3 the player wins $3. If the die shows 4, 5, 6 the player wins nothing. There is a charge of $1.25 to play this game. What is the game's expected value?
thank you!

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Question 220982: A single die is rolled twice. Find the probability of rolling an odd number the first time and a number less than 3 the second time.
thank you for your help!

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Question 220993: you draw one card from a 52-card deck. The card is replaced and the deck is reshuffled, then you draw a second card. Find the probability of drawing a 3 each time.
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Question 220992: You draw one card from a 52-card deck. The card is replaced and the deck is reshuffled, then you draw a second card. Find the probability of drawing a jack the first time and a club the second time.
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Question 220987: A single die is rolled twice. Find the probability of rolling a 5 the first time and a 1 the second time.
thank you for your help

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Question 221650: This problem stumps me..can u please explain how to work it??
The producer of All Things Considered, a radio-news program on NPR, has 4 in-depth and 8 short news stories for broadcast during the next two hours. The producer must arrange the in-depth and short stories by starting with an in-depth story followed by two short stories, and then another in-depth story and two short stories until all 12 stories have been aired. How many arrangements for the broadcast are possible?

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Question 221997: I'm brand new to this site. Can someone please give me a 30 second intro?

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Question 222300: Hello,
I'm good with solving direct and inverse but they threw in direct and inverse and I'm not quite sure how to treat this problem. Is it two problems?
Suppose z varies directly as the square of x and inversely as y. If z=8 when x=4 and y=6, find z when x=6 and y=12.
Thank you

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Question 223125: Playing deck of 52 cards. Select a card from the deck. What is the probability that the card will not be a face card? i have 40/52. 12 face cards minus the 12 face cards. am i close? if not could you explain how to get this answer. thanks ever so much.
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Question 223834: A store received a shipment of stuffed animals. The stockperson placed 1/5 of them on the shelves, leaving 280 of them in storage. How many of the items were in the shipment?
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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