Tutors Answer Your Questions about Permutations (FREE)
Question 1204818: A store is selling 7 types of hard candies: cherry, strawberry, orange, pineapple, apricot, blackberry, and lemon.
How many ways are there to choose:
(a) 17 candies?
Answer =
(b) 17 candies with at least a piece of each flavor?
Answer =
(c) 17 candies with at least 2 cherry and at least 3 lemon?
Answer =
Click here to see answer by ikleyn(52777)   |
Question 1204818: A store is selling 7 types of hard candies: cherry, strawberry, orange, pineapple, apricot, blackberry, and lemon.
How many ways are there to choose:
(a) 17 candies?
Answer =
(b) 17 candies with at least a piece of each flavor?
Answer =
(c) 17 candies with at least 2 cherry and at least 3 lemon?
Answer =
Click here to see answer by greenestamps(13198)  |
Question 1204817: A toys manufacture produces red, yellow, and green marples, with 8 available sizes, and containing or not a metal core.
a) How many different kinds of marples are available?
A boy has 7 red , 2 yellow and 5 green marbles. In how many ways can the boy arrange the marbles in a line if:
b) All marbles have different sizes?
c) Marbles of the same color are indistinguishable?
Click here to see answer by ikleyn(52777) |
Question 1204860: 11 books are to be stored in a shelf where 4 books can be put vertically, so they are all as easily accessible, and 6 books can be piled-up, so the most used ones are on the top.
(a) In how many ways the books can be put in vertical positions?
Your answer is :
(b) In how many ways the books can be piled-up?
Your answer is :
(c) In how many ways the books can be put in both positions?
Your answer is :
out of 11 books only 10 will be on the shelf.
Click here to see answer by ikleyn(52777) |
Question 1204860: 11 books are to be stored in a shelf where 4 books can be put vertically, so they are all as easily accessible, and 6 books can be piled-up, so the most used ones are on the top.
(a) In how many ways the books can be put in vertical positions?
Your answer is :
(b) In how many ways the books can be piled-up?
Your answer is :
(c) In how many ways the books can be put in both positions?
Your answer is :
out of 11 books only 10 will be on the shelf.
Click here to see answer by greenestamps(13198) |
Question 1205003: In a game room, there are three decks of cards: Deck 1 contains 5 red cards and 3 black cards, Deck 2
contains 3 red cards and 1 black card, and Deck 3 contains 4 red cards and 2 black cards. If a deck of
cards is selected at random, and then a card is drawn from the chosen deck, find the probability that
the drawn card will be red.
Click here to see answer by Edwin McCravy(20054)  |
Question 1205092: #1.
Prove for all integers n, k, and r with n ≥ k ≥ r that nCk×kCr = nCr×(n-r)C(k-r)
#2.
The binomial theorem states that for any real numbers a and b,
(a + b)n =∑_(k=0)^n▒〖(n¦k) a^(n-k) b^k 〗 for any integer n ≥ 0.
Use this theorem to show that for any integer n ≥ 0, ∑_(k=0)^n▒〖〖(-1)〗^k (n¦k) 3^(n-k) 2^k 〗 = 1.
Click here to see answer by mccravyedwin(406)  |
Question 1205092: #1.
Prove for all integers n, k, and r with n ≥ k ≥ r that nCk×kCr = nCr×(n-r)C(k-r)
#2.
The binomial theorem states that for any real numbers a and b,
(a + b)n =∑_(k=0)^n▒〖(n¦k) a^(n-k) b^k 〗 for any integer n ≥ 0.
Use this theorem to show that for any integer n ≥ 0, ∑_(k=0)^n▒〖〖(-1)〗^k (n¦k) 3^(n-k) 2^k 〗 = 1.
Click here to see answer by math_tutor2020(3816) |
Question 1205223: Freddie has forgotten the 6-digit code that he uses to lock his briefcase. He knows that he did not
repeat any digit and that he did not start his code with a zero.
(i) Find the number of different 6-digit numbers he could have chosen.
Freddie also remembers that his 6-digit code is divisible by 5.
(ii) Find the number of different 6-digit numbers he could have chosen.
Click here to see answer by ikleyn(52777) |
Question 1205797: Colby is the producer of the local talent competition show, Homegrown Superstars, and needs to form a panel of judges to evaluate performances. Colby has a list of 6 musicians and 8 actors from which to select the judging panel.
a. How many ways are there for Colby to select 5 judges, if the order does not matter?
b. If Colby randomly selects 5 judges, what is the probability that he will choose 2 musicians and 3 actors?
c. If Colby randomly selects 5 judges, what is the probability that at least one of them will be a actor?
Click here to see answer by ikleyn(52777) |
Question 1205803: according to a study conducted approximately 55% of all hospitals in a given town contained 100 or more beds. A researcher draws a sample of 15 hospitals by randomly selecting names from a directory of hospitals.
A.What is the probability of selecting 10 or more hospitals that have 100 or more beds?
B.What is the probability of selecting less than five hospitals that have 100 or more beds?
C.What is the probability of selecting from six to ten hospitals, inclusive, that have 100 or more beds?
Click here to see answer by Theo(13342)  |
Question 1206217: (a) How many seven-digit telephone numbers are possible if the first digit must be nonzero?
9000000
(b) How many international direct-dialing numbers for calls within the United States and Canada are possible if each number consists of a 1 plus a three-digit area code (the first digit of which must be nonzero) and a number of the type described in part (a)?
Click here to see answer by Edwin McCravy(20054) |
Question 1206241: So I really have no clue what to do for this question. The textbook asks for the coefficient of x. My thinking was that the coefficient should be 16, however, the answer is 96. The answer also calls for using Pascal's Triangle.
(2x+2)^4
Could someone please explain?
Click here to see answer by Theo(13342) |
Question 1206241: So I really have no clue what to do for this question. The textbook asks for the coefficient of x. My thinking was that the coefficient should be 16, however, the answer is 96. The answer also calls for using Pascal's Triangle.
(2x+2)^4
Could someone please explain?
Click here to see answer by greenestamps(13198) |
Question 1206240: So I really have no clue what to do for this question. The textbook asks for the coefficient of x. My thinking was that the coefficient should be 16, however, the answer is 96. The answer also calls for using Pascal's Triangle.
(2x+2)^4
Click here to see answer by Theo(13342) |
Question 1206240: So I really have no clue what to do for this question. The textbook asks for the coefficient of x. My thinking was that the coefficient should be 16, however, the answer is 96. The answer also calls for using Pascal's Triangle.
(2x+2)^4
Click here to see answer by math_tutor2020(3816) |
Question 1206362: 64 athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the 3 medals be distributed?
Click here to see answer by math_tutor2020(3816) |
Question 1206743: At a dinner party there are 10 people. They all sit at a round table. In how many ways can they sit if neither Amy nor Lucy want to sit next to Josh? I have tried this a few times and get a different answer each time. Can you help please?
Click here to see answer by ikleyn(52777) |
Question 1206815: Three hundred people apply for three jobs. 80 of the applicants are women.
(a) If three persons are selected at random, what is the probability that all are women? (Round the answer to six decimal places.)
(b) If three persons are selected at random, what is the probability that two are women? (Round the answer to six decimal places.)
(c) If three persons are selected at random, what is the probability that one is a woman? (Round the answer to six decimal places.)
(d) If three persons are selected at random, what is the probability that none is a woman? (Round the answer to six decimal places.)
(e) If you were an applicant, and the three selected people were not of your gender, should the above probabilities have an impact on your situation? Why?
Yes, the probabilities indicate the presence of gender discrimination.
No, because in the hiring process all outcomes are not equally likely.
Click here to see answer by ikleyn(52777) |
Question 1206897: Winning the jackpot in a particular lottery requires that you select the correct three numbers between 1 and 64 and, in a separate drawing, you must also select the correct single number between 1 and 27. Find the probability of winning the jackpot.
Click here to see answer by Theo(13342) |
Question 1206897: Winning the jackpot in a particular lottery requires that you select the correct three numbers between 1 and 64 and, in a separate drawing, you must also select the correct single number between 1 and 27. Find the probability of winning the jackpot.
Click here to see answer by ikleyn(52777) |
Question 1206918: An artist donates 3 different sculptures and 6 different vases to a museum. The exhibits will be arranged in a row. Find the number of possible arrangements if (a.) The 3 sculptures are placed together. (b.) The 3 sculptures are placed in the middle. (c.) Each sculpture must be placed between two vases.
Click here to see answer by Edwin McCravy(20054) |
Question 1206918: An artist donates 3 different sculptures and 6 different vases to a museum. The exhibits will be arranged in a row. Find the number of possible arrangements if (a.) The 3 sculptures are placed together. (b.) The 3 sculptures are placed in the middle. (c.) Each sculpture must be placed between two vases.
Click here to see answer by mccravyedwin(406) |
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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
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