Tutors Answer Your Questions about Permutations (FREE)
Question 1114331: How many different 5 digit numbers can be formed from the digit 1,2,3,4 and 5 if
(i). There are no restrictions on the digit and repetitions are allowed.
(ii). The number is odd and no repetition is allowed.
(iii).The number is even and reputation are allowed.
(iv). The number is greater than 50,000 and no repetitions are allowed.
Click here to see answer by Edwin McCravy(20054)   |
Question 1114461: How many different 5 digit numbers can be formed from the digit 1,2,3,4 and 5 if (i). They are no restriction on the digit and repetition are allowed. (ii). The number is odd and no repetition is allowed. (iii).The number is even and repetition are allowed. (iv). The number is greater than 50 000 and no repetition is allowed
Click here to see answer by ikleyn(52776)  |
Question 1114788: Hello, thank you for helping me with this math question
Consider a class with 12 girls and 10 boys (22 in total):
In how many ways can a committee of 5 consisting of 3 girls and 2 boys be chosen?
a) 0.03
b) 792
c) 0.3759
d) 9900
Here is my thought process which led to none of the given answer choices.
We can easily eliminate A and C, as they are not numbers of different arrangements, rather, they are probabilities, which is not what the question is asking.
I recognized the nature of the question to be a permutation, as you care about which order you are placing the 12 girls in 3 places on the committee. For example, Girl A, B, C is a possible permutation, but B, A, C is also a different permutation that must be counted. The same is true for putting the 10 boys into the 2 other spaces on the committee. So, I tried (12 nPr 3) + (10 nPr 2), which made logical sense in my head as you want 12 girls in 3 different ways on the committee plus the 10 boys you want in 3 different ways on the committee.
This way gets you to an answer of 1410, which is way off from the answer choices,so I was wondering what I did wrong in this thought process.
Thank you for your time and free advice :)
Click here to see answer by MathLover1(20849)  |
Question 1114788: Hello, thank you for helping me with this math question
Consider a class with 12 girls and 10 boys (22 in total):
In how many ways can a committee of 5 consisting of 3 girls and 2 boys be chosen?
a) 0.03
b) 792
c) 0.3759
d) 9900
Here is my thought process which led to none of the given answer choices.
We can easily eliminate A and C, as they are not numbers of different arrangements, rather, they are probabilities, which is not what the question is asking.
I recognized the nature of the question to be a permutation, as you care about which order you are placing the 12 girls in 3 places on the committee. For example, Girl A, B, C is a possible permutation, but B, A, C is also a different permutation that must be counted. The same is true for putting the 10 boys into the 2 other spaces on the committee. So, I tried (12 nPr 3) + (10 nPr 2), which made logical sense in my head as you want 12 girls in 3 different ways on the committee plus the 10 boys you want in 3 different ways on the committee.
This way gets you to an answer of 1410, which is way off from the answer choices,so I was wondering what I did wrong in this thought process.
Thank you for your time and free advice :)
Click here to see answer by greenestamps(13198)  |
Question 1114788: Hello, thank you for helping me with this math question
Consider a class with 12 girls and 10 boys (22 in total):
In how many ways can a committee of 5 consisting of 3 girls and 2 boys be chosen?
a) 0.03
b) 792
c) 0.3759
d) 9900
Here is my thought process which led to none of the given answer choices.
We can easily eliminate A and C, as they are not numbers of different arrangements, rather, they are probabilities, which is not what the question is asking.
I recognized the nature of the question to be a permutation, as you care about which order you are placing the 12 girls in 3 places on the committee. For example, Girl A, B, C is a possible permutation, but B, A, C is also a different permutation that must be counted. The same is true for putting the 10 boys into the 2 other spaces on the committee. So, I tried (12 nPr 3) + (10 nPr 2), which made logical sense in my head as you want 12 girls in 3 different ways on the committee plus the 10 boys you want in 3 different ways on the committee.
This way gets you to an answer of 1410, which is way off from the answer choices,so I was wondering what I did wrong in this thought process.
Thank you for your time and free advice :)
Click here to see answer by ikleyn(52776) |
Question 1114856: Five different algebra textbooks, two different calculus textbooks, and four different geometry textbooks are to be arranged on a shelf. How many different arrangements are possible if the books of each subject must be kept together?
Click here to see answer by stanbon(75887) |
Question 1114856: Five different algebra textbooks, two different calculus textbooks, and four different geometry textbooks are to be arranged on a shelf. How many different arrangements are possible if the books of each subject must be kept together?
Click here to see answer by math_helper(2461)  |
Question 1114945: A bookseller has 10 identical books of math 101, 3 identical books of Acc 201, and 5 identical books of Stat 102. In how many different ways can he display his books?(Note that the books in same subject are identical, one cannot be differed from others)
Click here to see answer by ikleyn(52776) |
Question 1115360: A fifth-year student has to choose 4 subjects from the following list: Accounting, Biology,Chemistry, Physics, French, Applied Maths and Classical Studies. (i) How many different choices are possible. (ii) How many choices include french? (iii) How many choices do not include french? (iv) How many choices include Accounting and Biology? (v) How many choices include Applied Matjs but not Chemistry?
Click here to see answer by stanbon(75887) |
Question 1115533: Seven cheerleaders line up to enter a gym at the start of a basketball game. Three carry signs and four carry pom-poms. How many different ways can they form their line if the first in line and the last must be sign carriers?
Click here to see answer by ikleyn(52776) |
Question 1115779: One fateful evening, seven different fires erupt around town. The local fire station houses 21 distinct fire trucks. The fire chief is instructed to dispatch exactly three trucks to fight each of the blazes. In how many ways can the trucks be dispatched ?
Click here to see answer by ikleyn(52776) |
Question 1115780: One fateful evening, seven different fires erupt around town. The local fire station houses 21 distinct fire trucks. The fire chief is instructed to dispatch exactly three trucks to fight each of the blazes. In how many ways can the trucks be dispatched ?
In the above problem, suppose the fire chief is to dispatch all 21 trucks, but there are no requirements on how many trucks must visit any given fire. Now how many choices does the fire chief have ?
Click here to see answer by ikleyn(52776) |
Question 1115716: In how many ways can a party of 6 children be chosen from a group of 10 children if if:(i) any child may be selected? (ii) the oldest child must not be selected? (iii) the youngest child must be selected? (iv) the youngest and the oldest must both be selected
Click here to see answer by MusabShakeel(1) |
Question 1115716: In how many ways can a party of 6 children be chosen from a group of 10 children if if:(i) any child may be selected? (ii) the oldest child must not be selected? (iii) the youngest child must be selected? (iv) the youngest and the oldest must both be selected
Click here to see answer by ikleyn(52776) |
Question 1115831: There are 15 pupils in a class. How many teams of 11 can be selected from the class? If one person in the class is made captain and must always be included in each team, how many teams can now be selected? If 2 pupils in the class refuse to play, how many teams can now be selected, if the captain must still be on every team.
Click here to see answer by ikleyn(52776) |
Question 1115877: A painter has 12 colors of paint available. When painting a house, the painter needs to choose a main color, trim color, accent color and siding color, and all of the must be different from one another. How many ways are there for the painter to pick colors for the house ?
My work :
12P4 = 11880
Click here to see answer by greenestamps(13198) |
Question 1115877: A painter has 12 colors of paint available. When painting a house, the painter needs to choose a main color, trim color, accent color and siding color, and all of the must be different from one another. How many ways are there for the painter to pick colors for the house ?
My work :
12P4 = 11880
Click here to see answer by ikleyn(52776) |
Question 1115874: You are making goodie bags for your next birthday party. You have an assortment of 10 different toys and candy to put in the bag. If you want to put 7 items in each bag, how many different goodie bags can you make ?
My work :
10C7 = 120
Click here to see answer by ikleyn(52776) |
Question 1115938: A music class of eight girls and seven boys is having a recital. If each member is to perform once, how many ways can the program be arranged in each of the following cases:
a) The girls must all perform first.
b) A girl must perform first and a boy must perform last.
c) The entire program will alternate between girls and boys, starting with a girl.
d) The first, eighth, and fifteenth performers must be girls.
Click here to see answer by stanbon(75887) |
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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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