Tutors Answer Your Questions about Permutations (FREE)
Question 1149524: A carton contains 15 transistors of which 5 are defective. If a random sample of 6 transistors are drawn from the carton (without replacement) determine the probability of 2 defective valves in the sample.
Click here to see answer by ikleyn(52776)   |
Question 1149904: When Mendel crossed a tall plant strain of pea with a dwarf strain of pea, he found that 3/4 of the offspring were tall and 1/4 were dwarf. Suppose 5 such offspring were tall;
(i) all these offsprings were tall
(ii) at least three of these offspring were tall.
Click here to see answer by ikleyn(52776) |
Question 1149900: one-fifth of all jellybeans are black. A random sample of ten jellybeans is chosen.
What is the probability that this sample contains exactly two jellybeans?
What is the probability that it contains fewer than two black beans?
Click here to see answer by Boreal(15235)  |
Question 1150272: There are 6 men and 4 women in club. A team of 4 members has to be
chosen. Find the number of different ways of selecting the team if:
a) All the members are to be of the same sex.
b) There must be an equal number of men and women. Given that the 4 women include 2 sisters, find the total number of ways in which the team can be selected if either of the sisters, but not both, must be included.
Click here to see answer by VFBundy(438)  |
Question 1150509: With the help of permutations:
Consider all positive integers with three different digits. (Note that zero cannot be the first digit.) Find the number of
them which are: (a) greater than 700; (b) odd; (c) divisible by 5.
Click here to see answer by ikleyn(52776) |
Question 1150816: The problem is: Find the number of ways in which four girls and three boys can
arrange themselves in a row so that none of the boys are together?
There are two possible solutions but only one is considered.
The first one, in which I made, is that, we can lay the three boys firstly in
the row, making it _B1_B2_B3_. Since there are 4 spaces, in each space we can
permute the girls. Thus the solution is 4!*3!=144 ways
Now the second one, we can lay the four girls before the boys, leaving blank
spaces for the boys at this configuration: _G_G_G_G_. Since there are 5 blanks,
boys can choose their positions giving it a 5P3. By multiplication, the answer
is 5P3*4!=1440 ways
And to conclude, the right answer,at most it would be considered,is the second
one, 1440 ways. My question is why the first one is not the right answer? At
what fair reason should it be accounted? Did I undercount, and/or make a gap in
my logic? Hope to shed a clear explanation on my question. Thank you.
Click here to see answer by Edwin McCravy(20054)  |
Question 1150858: A classroom has 71 students. Ten of them are Chinese, 24 are Japanese, and 37 are Filipinos. If three are randomly picked to get out from the room, one after the other, what are the possibilities that all three are Chinese?
Click here to see answer by ikleyn(52776) |
Question 1150911: The English alphabet has 26 letters of which 5 are vowels. Consider only 5-
letter “words” consisting of 3 different consonants and 2 different vowels. Find
the number of such words which:
(a) have no restrictions;
(c) contain the letters B and C;
(b) contain the letter B;
(d) begin with B and contain the letter C.
Click here to see answer by Edwin McCravy(20054) |
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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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