Tutors Answer Your Questions about Permutations (FREE)
Question 1174660: If the team has four golf clubs it wants to give to its three players.
1) How many ways can you distribute the clubs?
2) How many options are there if suit number 1 should be for the first player and for number 3 it should be for the second or third player?
Click here to see answer by CPhill(1959)   |
Question 1173392: In a school, every grade 10 student need to study 7 subjects out of 14. It is given that 4 of them are core subject, and the rest are optional. How many arrangements of the subjects are available for the students?
Click here to see answer by CPhill(1959) |
Question 1173392: In a school, every grade 10 student need to study 7 subjects out of 14. It is given that 4 of them are core subject, and the rest are optional. How many arrangements of the subjects are available for the students?
Click here to see answer by ikleyn(52776)  |
Question 1165571: Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Which of the following best describes the form of the sampling distribution of the sample mean for this situation?
Click here to see answer by ikleyn(52776) |
Question 1210160: Suppose for this problem (though it may not be accurate in real life) that the Senate has 48 Republicans and 52 Democrats. In how many ways can we form a committee with 5 senators, in which neither party holds all 5 seats?
Click here to see answer by CPhill(1959) |
Question 1210162: Now suppose that not only must Sir Lancelot and Sir Gawain be next to each other, but Sir Galahad and Sir Percival also demand to be next to each other. How many seatings of the 8 knights are possible?
Click here to see answer by CPhill(1959) |
Question 1210172: Given a regular octagon, in how many ways can we color one diagonal red and another diagonal blue so that the two colored diagonals intersect at an endpoint? Consider rotations and reflections distinct.
Click here to see answer by CPhill(1959) |
Question 1210179: A survey conducted among 150 high school students revealed that
* 68 students like Math
* 85 students like English
* 55 students like History
* 20 students like both Math and English
* 15 students like both Math and History
* 22 students like both English and History
* 8 students like all three subjects
How many students like at least one subject?
Click here to see answer by CPhill(1959) |
Question 1210179: A survey conducted among 150 high school students revealed that
* 68 students like Math
* 85 students like English
* 55 students like History
* 20 students like both Math and English
* 15 students like both Math and History
* 22 students like both English and History
* 8 students like all three subjects
How many students like at least one subject?
Click here to see answer by ikleyn(52776) |
Question 1210181: If an ant crawls from one corner to the other corner of a 3 \times 5 rectangle, then it will cross through seven squares.
If the ant crawls from one corner to the other corner of a 15 \times 16 rectangle, then how many squares will it cross through?
Click here to see answer by CPhill(1959) |
Question 1210182: A permutation of the numbers (1,2,3,\dots,n) is a rearrangement of the numbers in which each number appears exactly once. For example, (2,5,1,4,3)$ is a permutation of (1,2,3,4,5).
Let \pi = (x_1,x_2,x_3,\dots,x_n) be a permutation of the numbers (1,2,3,\dots,n). A fixed point of \pi is an integer k, 1 \le k \le n, such that x_k = k. For example, 4 is a fixed point of the permutation (2,5,1,4,3).
How many permutations of (1,2,3,4,5,6,7) have at least four fixed point?
Click here to see answer by CPhill(1959) |
Question 1210184: I can only remember a seven-digit telephone number if the first three digits (the "prefix") are equal to the next three digits or the last three digits. For example, I can remember 389-3892 and 274-9274.
How many seven-digit telephone numbers can I remember?
(For this problem, a telephone number cannot start with a 0.)
Click here to see answer by CPhill(1959) |
Question 1210184: I can only remember a seven-digit telephone number if the first three digits (the "prefix") are equal to the next three digits or the last three digits. For example, I can remember 389-3892 and 274-9274.
How many seven-digit telephone numbers can I remember?
(For this problem, a telephone number cannot start with a 0.)
Click here to see answer by ikleyn(52776) |
Question 1210194: At a meeting, two scientists, two mathematicians, two historians, and two artists are to be seated around a circular table. In how many ways can they be seated so that all four pairs of people from the same discipline are seated together?
Click here to see answer by CPhill(1959) |
Question 1210194: At a meeting, two scientists, two mathematicians, two historians, and two artists are to be seated around a circular table. In how many ways can they be seated so that all four pairs of people from the same discipline are seated together?
Click here to see answer by ikleyn(52776) |
Question 1210198: A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit.
You are dealt a hand of 13 cards. Find the probability that your hand has a void. (Your hand has a void if it does not contain any cards of a particular suit.)
Once you've computed the answer in terms of binomial coefficients, use a calculator or computer to determine the answer to the nearest tenth of a percent, and enter that as your answer.
Click here to see answer by CPhill(1959) |
Question 1210198: A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit.
You are dealt a hand of 13 cards. Find the probability that your hand has a void. (Your hand has a void if it does not contain any cards of a particular suit.)
Once you've computed the answer in terms of binomial coefficients, use a calculator or computer to determine the answer to the nearest tenth of a percent, and enter that as your answer.
Click here to see answer by greenestamps(13198)  |
Question 1210199: Find the number of sequences (a_1, a_2, a_3, \dots, a_8) such that:
* a_i \in \{1, 2, 3, 4, 5, 6, 7, 8\} for all 1 \le i \le 8.
* Every number1, 2, 3, 4, 5, 6, 7, 8 appears at least once in the sequence.
Click here to see answer by CPhill(1959) |
Question 1210199: Find the number of sequences (a_1, a_2, a_3, \dots, a_8) such that:
* a_i \in \{1, 2, 3, 4, 5, 6, 7, 8\} for all 1 \le i \le 8.
* Every number1, 2, 3, 4, 5, 6, 7, 8 appears at least once in the sequence.
Click here to see answer by greenestamps(13198) |
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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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