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Question 1100891: suppose the supervisor in our previous example wished to have an ID card with two letters and two digits. how many different ID cards could be made?
Click here to see answer by ikleyn(52776)

Question 1100927: How many positive integers less than 1000
a) have exactly three decimal digits?
b) have an odd number of decimal digits?
c) have at least one decimal digit equal to 9?
d) have no odd decimal digits?
e) have two consecutive decimal digits equal to 5?
f ) are palindromes (that is, read the same forward and backward)?
Click here to see answer by Alan3354(69443)

Question 1100926: Find n c. P(n, 4) = 12P(n, 2)
d) C(n, 2) = 45 e) C(n, 3) = P(n, 2) f) C(n, 5) = C(n, 2).

Click here to see answer by ikleyn(52776)

Question 1101050: A teacher makes a multiple-choice quiz with 12 questions. 3 answers are A, 3 answers are B,2 answers are C and 4 answers are D. How many possible answer keys are possible
I think you can solve it like this but am not sure:
12C3 x 9C3 x 6C2 x 4C4
= 277200 keys
Click here to see answer by rothauserc(4718)

Question 1101364: I have two fair dice. If I throw both dice at the same time, what is the chance (as fraction) of getting a sum of 8?
Click here to see answer by math_helper(2461)

Question 1101604: If 4 delegates are to speak at a convention on how many ways can they speak
Click here to see answer by Boreal(15235)

Question 1101680: Please help me to solve this.
In a poker hand consisting of 5 cards, what is the probability of holding 2 Aces and 3 Kings?
Click here to see answer by Edwin McCravy(20054)

Question 1101680: Please help me to solve this.
In a poker hand consisting of 5 cards, what is the probability of holding 2 Aces and 3 Kings?
Click here to see answer by Theo(13342)

Question 1101957: A team composed of two grade11 and two grade 10 students is to be sent to a debate contest. If there are 60 grade 10 and 55 grade 11 students, in how many ways can the selection of students for the contest be done?

Click here to see answer by ikleyn(52776)

Question 1102052: A class consists of 15 men and 17 women. Find the number of ways that the people in the class can arrange themselves in the following cases. (i) How many groups can be chosen from this class which consists of 7 men and 10 women?
Answer: C(15,7) * C(17,10) = 125147880
(ii)If two students have to be in the same group, how many groups of 12 students can be formed from this class?
Answer: 1 x C(30,10) + C(30,12) =
(iii) If one male A and one female B cannot be in the same committee, how many ways can a committee consisting of 4 men and 4 women be chosen from the class?
Answer: A committee consisting of 4 men and 4 women:
C(15,4) * C(17,4) = 3248700
From 3248700 subtract the cases where that male A and female B in the same committee. In those case we choose 3 men from the other 14 and 3 women from the other 16, so the number must subtract is:
C(14,3) * C(16,3) =364 * 560 = 203840 => 3248700 - 203840 = 3044860
Click here to see answer by ikleyn(52776)

Question 1102188: in a dance contest, each participating group must perform 3 kinds of dance. if there are 4 choices for ballroom dance, 8 choices for foreign dance, and 5 choices for hip hop. in how many possible ways can a dance group select their piece?
Click here to see answer by Boreal(15235)

Question 1102191: in how ways can 5 boys and 3 girls be arranged in a circle if the girl must stand together

Click here to see answer by greenestamps(13198)

Question 1102191: in how ways can 5 boys and 3 girls be arranged in a circle if the girl must stand together

Click here to see answer by ikleyn(52776)

Question 1102189: there are identified points on a number line. how many possible rays can be drawn using the given points?

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Question 1102395: How many numbers less than 9000 contain only 6, 7 or 8 as digits?
Click here to see answer by KMST(5328)

Question 1102309: 2 math books,4 science books and 3 literature books are to be arranged on a shelf. In how many ways can this be done if the 2 math books are not together?
Click here to see answer by math_helper(2461)

Question 1102636: In how many ways can a club consisting of 12 members choose a president, a sectary and a treasurer?
Click here to see answer by Alan3354(69443)

Question 1102725: How many different committees can be formed from 7 teachers and 9 students if the committee is to consist of 3 teachers and 4 students?
Click here to see answer by math_helper(2461)

Question 1102735: A project team of 2 to 5 people is being formed from a staff of 15. How many such teams are possible
Click here to see answer by Boreal(15235)

Question 1102844: In how many ways can 6 persons sit down on 8 chairs in a straight line?
Click here to see answer by ikleyn(52776)

Question 1102843: Let n and r be positive integers with n ≥ r. Prove that rCr + (r+1Cr)+...+( nCr) = (n+1Cr+1)
Click here to see answer by math_helper(2461)

Question 1102970: a club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 9 members to choose from?

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Question 1103310: Suppose u originally paid $1000 in taxes. During year 1, taxes decrease by 20%. During year 2, taxes increase by 20%. A=how do your taxes for year 2 compare with the $1000 u originally paid? B= find the percent increase or decrease from the original $1000 to year 2 taxes.
Click here to see answer by stanbon(75887)

Question 1103308: U r getting married in 2 years.
Click here to see answer by richwmiller(17219)

Question 1103434: in how many ways can five couples be seated in a row if
a. there are no restrictions?
b. each couple must be seated together?
c. each husband must be seated to the left of his wife?
Click here to see answer by ikleyn(52776)

Question 1103609: Suppose you have an urn containing 7 red and 3 blue balls. You draw three balls at random. On each draw, if the ball is red you set it aside and if the ball is blue you put it back in the urn. What is the probability that the third draw is blue? (If you get a blue ball it counts as a draw even though you put it back in the urn)
Click here to see answer by Edwin McCravy(20054)

Question 1103433: in how many ways can a research team of 5 members be formed from a group consisting of 3 chemist and 7 physicist if
a. there is no restriction in the selection?
b. the team must include exactly 2 chemist?
c. the team must include at most 3 physicists?
Click here to see answer by Boreal(15235)

Question 1103688: a photographer arranges 126 students for a class picture. Each row has the same numbers of students. what numbers of rows can he make?

Click here to see answer by josgarithmetic(39616)

Question 1103709: The number of arrangements that can be formed by taking all the letters of the word CHEESE so that no two Es come together
Click here to see answer by Edwin McCravy(20054)

Question 1103936: This diagram shows the aerial view of a playground. What is the area of the playground to the nearest square yard? Use the value = 3.14.
Click here to see answer by Alan3354(69443)

Question 1103976: 4. A password
5.
6
Click here to see answer by richwmiller(17219)

Question 1103975: 1.
2.
3.
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Question 1103979: 3. A certain password consist of 3 different letters of the alphabet where each letter is used only once. How many different possible passwords are there?
Click here to see answer by Alan3354(69443)

Question 1104018: Consider the distinguishable arrangement of the 12 letters in FRANKINCENSE.
a) How many arrangements are there in total?
I understand this one, 12!/2!3!, however I cannot answer the next part,
b) How many arrangements have all three N's together, and have two E's separated?
I would have guessed the answer is 10! 11c2 as the N;s are grouped together, and there are 11 chose 2 spots for the E's
Thank you :)
Click here to see answer by ikleyn(52776)

Question 1104078: There are 15 players. In how many ways can you select 5 players, and the captain should be involved?
Click here to see answer by Edwin McCravy(20054)

Question 1103464: you are transferring to a new house. You have a collection of books but you can not take them all with you. In how many ways can you select 7 books out of 10,and then arrange these books on a shelf if there is space enough for only 5 books?
Click here to see answer by Edwin McCravy(20054)

Question 1104087: hi Algebra.Com tutors,
thanks for your mathematical services. I have been dealing with permutations for a while, so I'm a genius at solving them, I believe.
however, the problem challenging me is working them practically! I solved 3 P 2 (=6) by drawing a table. But 5 P 3 (=60) and 10 P 3 (=720) failed completely!
Can you help me with the true table proving the results above?
I look forward to hear from you.

A. S. B. H.
Click here to see answer by rothauserc(4718)

Question 1104062: Homecoming has 7 candidates for King and 6 candidates for Queen. How many King, Queen, and two First Runner-ups can be chosen to form the Festival Court?
Click here to see answer by Edwin McCravy(20054)

Question 1104166: A man has 10 shirts and 7 ties. How many different shirt and tie arrangements can he wear?

Click here to see answer by ikleyn(52776)

Question 1104217: Hello! If I could get help with the following question:
An organization can elect a president and a different secretary in 210 different ways. How many members does the organization have?
Thank you!
Click here to see answer by greenestamps(13198)

Question 1104497: Which term in the expansion of (A+B)^25 has the same coefficient as the term 23? (Please show your step by step work).
Click here to see answer by Edwin McCravy(20054)

Question 1104543: A librarian chooses seven holiday books from a selection of ten to be displayed in the window of the library. In how many different ways can she choose the group of seven books?
Click here to see answer by ikleyn(52776)

Question 1104692: A particular shirt style comes in 4 colors. Each color comes in 6 sizes and each size comes in 7 sleeve lengths. If a retailer wanted to have all in stock how many different shirts would have to be stocked?
Click here to see answer by ikleyn(52776)

Question 1104831: Q.1 How many ways can 4 teddy bears , 3 toy trucks , 5 dolls and 1 toy cars be distributed among 13 children if each child is to receive 1 item?
Q.2 In a group of 14 students there are 8 girls and 6 boys.
The committee of 4 students must have 1 girl and 1 boy and 2 other students, how many different committees can be chosen from this group?
Click here to see answer by stanbon(75887)

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