Questions on Algebra: Combinatorics and Permutations answered by real tutors!

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Question 87331: How many ways can 12 people out of 300 be selected for a jury?
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Question 87332: Please assist me with solving this.
Rosa's serves 11 appetizers, 26 main courses, 8 desserts, and 11 beverages. How many dinner combinations can be made if each includes one of each?
thanks!

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Question 87500: Thank you for any help you can give me.
If liscense plates are formed by 3 letters followed by 4 digits, how many different liscense plates can be made?
10 digits (0-9)
26 letters

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Question 87547: How may different 5-digit numbers that are odd and less than 50,000 can be formed using the digits 2,3,4,5,6,7 and 8 without repetition?
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Question 88720: in how many ways can you make a four-letter password from A, B, C, D, E if you are not allowed to repete characters?
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Question 88731: a club with 10 members is to pick a president, vice president, treasurer, and secretary. If each office is to be held by one person and no person can hold 2 offices, in how many ways can those offices be filled?
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Question 88734: find the value of the expression 12P4
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Question 88734: find the value of the expression 12P4
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Question 88733: find the value of the expression 10C8
--------
10C8 is the same as 10C2
10C2 = [10*9]/[1*2] = 45
============================
Cheers,
Stan H.

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Question 88733: find the value of the expression 10C8
--------
10C8 is the same as 10C2
10C2 = [10*9]/[1*2] = 45
============================
Cheers,
Stan H.

Click here to see answer by stanbon(26291) About Me 

Question 88729: A car is available is three types of models and in three colors. In how many cobinations can you buy the car?
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Question 88730: A test has 10 true/false questions. How many different tests can be turned in to the teacher?
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Question 88730: A test has 10 true/false questions. How many different tests can be turned in to the teacher?
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Question 88821: Please find the value of the expression 4P4
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Question 88823: Please find the value of 12C4
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Question 88825: Please
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Question 90656: WHAT ARE ALL THE DIFFERENT 4 DIGIT COMBINATIONS THAT CAN BE MADE FROM THE NUMBERS 1-9 ?
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Question 90844: In how many ways can a baseball coach arrange the batting order. There are 9 players?

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Question 90847: In how many ways can a full house of three aces and two kings be obtained?
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Question 90846: What is the probability of drawing three aces from a deck of cards if three cards are drawn at random?
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Question 90845: Suppose four cards are drawn from a deck of cards. In how many ways can four aces be drawn?

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Question 90842This question is from textbook
: A bag contains 12 pieces of candy, five of which are lemon drops. If you reach in and select one piece of candy at random, what is the probability it is a lemon drop?This question is from textbook

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Question 90927: calculate this factorial 140!
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Question 90843: a bag contains 12 pieces of candy, five of which are lemon drops. If you reach in and select two pieces of candy. What is the probability they will both be lemon drops?

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Question 91014: A total of 14 people - 8 men and 6 women have applied for admission to a business school. The school has 5 openings.
a. How many ways are there of selecting the students to be admitted?
b. How many ways are there if at least 4 of them must be women?
c. How many ways are there if at least 3 of them must be women?
d. How many ways if exatly 3 of them must be men?
e. How many ways if at least one of them must be a man?
Thank you all for your help. I appreciate it!

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Question 91844: an 8 bit string is an 8-character long string where each character is either a 0 or 1. How many 8-bit strings have exactly three 1's?
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Question 91984: In how many ways can four identical 25c stamps books, two identical 50c and three identical 75c stamps be arranged in a line along the top of an envelope?
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Question 91983: in how many ways can we seat three of five boys and three of five girls if boys and girls must alternate?
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Question 92264: Please explain thoroughly the solutions to the following questions. thanks. :)
Consider placing three(3) balls into three(4) boxes labeled A, B, and C. In how many ways can this be done
a) if the three balls are of the same color and each box can hold at most one ball?
b) if the three balls are of the same color and each box can hold at most three balls?

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Question 92263: Please help me. Please explain the answers/solutions to the following questions thouroughly. thanks
In how many ways can a committee of six(6) members be selected from ten(8) students, namely, A, B, C, D, E, F, G and H, so that
a) at least one of the students A, F, and H will be included in the committee?
b) not one of A, F, and H is included in the committee?

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Question 92750: Please help me explain thoroughly the answer to the following questions? thank you so much
Consider a multiple-choice exam with 15 items and each item has 3 choices. and a student must answer all the items:
a) in how many ways can the student answer it and all his/her answers are correct?
b.) In how many ways can a student answer the exam and answer exactly four items correctly?
c) In how many ways can a student answer the exam and answer at least one(1) item correctly?

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Question 92835: A license plate number consists of 1,2 or 3 capital letters followed by 4 digits (ranging from 0 to 9). Some possible care license plate numbers are B1930, C2970, YO4001, DUH2093. HOW MANY PSSIBLE LICENSE PLATE NUMBERS ARE THERE
a: if repetition of letters and digits is allowed
b: if repetetion of letters and digits is not allowed

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Question 92887: M needs to choose seven different pairs of shoes from her collection of twelve(12) pairs to wear during the week. In how many ways can she do this
a) if she simply wants to select seven pairs
b) if the first pair she selects will be worn on Sunday; the second pair on monday; the third on tuesday and so on..
Need help ASAP.. thanks really.. appreciate it

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Question 92850: Anna has 12 pairs of shoes and she needs to choose seven different pairs to wear during the week. In how many ways can she do this:
a) if she simply wants to select seven pairs
b) if the first pair she selected will be worn on Sunday, the second on Monday; the third on Tuesday and so on..

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Question 93259: I would like to see step by step how this problem is solved 3|2x+5|-2<18
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Question 93300: The menu at a restaurant has 11 appetizers, 15 entrees, 10 desserts, and 8 beverages. The restaurant offers a dinner special that includes 1 appetizer, 1 entree, 1 dessert, and 1 beverage. In how many ways can a person order a dinner special at this restaurant?
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Question 93300: The menu at a restaurant has 11 appetizers, 15 entrees, 10 desserts, and 8 beverages. The restaurant offers a dinner special that includes 1 appetizer, 1 entree, 1 dessert, and 1 beverage. In how many ways can a person order a dinner special at this restaurant?
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Question 93336: C(15,6)
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Question 93339: C(8,8)P(8,8)C(7,2)
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Question 93530: Combinations
Question: Find the number of ways in which each committee can be selected.
1. a committe of 5 people from a group of 8 people
2. a committe of 2 people from a group of 16 people
3. a committe of 4 people from a group of 7people
4. a committe of 8 people from a group of 15people
5. a committe of 3 people from a group of 8 people
Question: At luncheon guest are offered a selection of 4 diffrent grilled vegetables and 5 diffrent relishes. In how many ways can the following items be chosen?
6. 2 vegetables and 3 relishes
7. 3 vegetables and 2 relishes
8. 4 vegetables and 4 relishes
9. 3 vegetables and 3 relishes
Question: A bag contains 8 white marbles and 7 blue marbles. Find the probability of selecting each combination
10. 2 white and 3 blue
11. 3 white and 2 blue
12. 4 white and 1 blue

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Question 93528: Permutations
1. taking all 7 letters at a time
2. taking 5 letts at a time
3. taking 4 letters at a time
4. taking 3 letters at a time
Question: in how many ways can 12 books be displayed on a shelf if the given number of books are available?
5. 12 books
6. 14 books
7. 15 books
8. 20 books
Question: Find the number of permutations of the letters in each word.
9. geometry
10. algebra
11. addition
12. calculus
13. mathematics
14. arithmetic

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Question 93418: 1) How many phone numbers in Chicago can have the area code 312?
I am stuck on this problem. I figure that there are 10 numbers from 0 to 9 and that 0 and 1 are not used at all, therefore, this leaves 8 digits. This is as far as I have gotten.

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Question 93736: 1. A committee of four people is to be chosen from a group of five women and six men. In how many ways can this be done if:
a. There are no restrictions
b. The committee is to have exactly two men?
c. The committee is to have at most two men?
2. A jar contains six black and five white marbles. Two marbles are drawn from the jar without replacement. Find the indicated probabilities.
a. P(two white marbles)
b. P(one white and one black marble)
Thank you so much!

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Question 93735: Evaluate 9P2
Evaluate 9C2
A group of three men and two women are to be seated in a row of five chairs. In how many ways can this be done if:
a. There are no restrictions?
b. The men and women must alternate?
c. The two women must be seated at the ends of the rows?
Thank you so much for your help! Caroline

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Question 94231: how do you evaluate this equation step by step: 6!-4!
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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