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

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 Algebra: Combinatorics and Permutations Solvers Lessons Answers archive Quiz In Depth

 Question 72163: I need help with this problem, it is multiplying and dividing factorials. In case you cannot tell: /= Division *= Multiplication 6!/2!4! * 5!/4!1! Thank you! Click here to see answer by jim_thompson5910(28595)

 Question 72454: Determine the constant term in the expansion of (2x-2/5x^2)^8. I am doing this math independently. I have looked through my textbooks, but cannot find what a consant term is. I have expanded this by binomial expansion but there is not one constant term in the solution as all constants are differnt numbers with differnt x values. Thank you Kristen Click here to see answer by Edwin McCravy(8909)

 Question 72460: Determine the coefficent of the term containing a^5 in the expansion of (a - 1/a)^5 I got 1 for the coefficent of a^5. However, I can not read my teachers writing and I think that the the question could be, "Determine the coefficent of the term containing a in the expansion of (a - 1/a)^5". If this is the case I am not sure of the coefficent since there are two a's and when you expand using binomial expansion, there are two possible terms that have a values (either multipy the a's together to get a or there is just an a in one of the terms). Thank you, Kristen Click here to see answer by stanbon(57361)

 Question 72458: Determine the eight term (simplified) in the expansion of (4a+7b)^15. Thank you Kristen Click here to see answer by stanbon(57361)

 Question 72469: Hi, I am resubmitting this question, as it might be confusing. Determine the constant term in the expansion of I am doing this math independently. I have looked through my textbooks, but cannot find what a consant term is. I have expanded this by binomial expansion but there is not one constant term in the solution as all constants are differnt numbers with differnt x values. Thank you Kristen Click here to see answer by psbhowmick(529)

 Question 74205: I have the following problem: Let P(n, k) denote the number of permutations of k objects selected from a set of n. We have the formula P (n,k) = n!/(n-k)! Prove that for all integers n>or=2, P(n+1,2)-P(n, 2)=2P(n, 1). I did some research on factorial identities and got a little further, but I'm not getting to the desired end result. I guess where I'm most stuck is the goal -- is 2P(n,1) equal to 2(n!/(n-1)!)? I've never seen the '2P' before. Thanks! Click here to see answer by stanbon(57361)

 Question 74411: A restaurant offers a choice of 3 appetizers, 6 main dishes, 7 desserts, and 5 beverages. How many complete dinners are available? Click here to see answer by Cintchr(481)

 Question 76118: A hand of 12 cards is dealt from a well- shuffled standard 52 card deck of cards. What is the probability that the hand contains 4 jacks? Click here to see answer by stanbon(57361)

 Question 76116: A coin is tossed 9 times. What is the probability that the coin will land heads at least 7 times? Click here to see answer by stanbon(57361)
 Question 76116: A coin is tossed 9 times. What is the probability that the coin will land heads at least 7 times? Click here to see answer by Edwin McCravy(8909)

 Question 76400: My question is about adding factorials. This seems easy but not sure. Question is 9! + 4! I understand that the nine is 9 8 7 6 5 4 3 2 1 then the 4 is 4 3 2 1 do you just add the numbers?????? Or what? Thanks, Gary Click here to see answer by jim_thompson5910(28595)

 Question 77763: I get10X 5040 =50400 is this right? In how many ways can a phone number be created if there are ten ways that the first three digits can be arranged and then each of the remaining four digits canbe any digit from 0-9 as long as no digit is repeated in the group of 4? Click here to see answer by stanbon(57361)

 Question 80736: If the first three digits of someone's phone number (do not include area code) are 777, How many different phone numbers could they have? Please don't just give me and answer. I would like to know how to work this problem. I know that there 7digits in a phone numer, and the first three digits are taken then there are 4digits availiable. is it P=n/(n-r)! where n=7 and r=4 I am not sure. Click here to see answer by stanbon(57361)

 Question 83527: In how many ways can 5 books be arranged on a shelf? Click here to see answer by stanbon(57361)

 Question 83529: A three-digit number is formed by selecting from the digits 1,2,3,4,5 and 6 with no repitition. How many of these three digit numbers will have a number greater than 300? Click here to see answer by Edwin McCravy(8909)

 Question 83645: In the four periods before lunch, Sally will take math, english, italian, and biology. In how many ways can Sally's program be arranged? Click here to see answer by checkley75(3666)

 Question 83646: In how many ways can we elect 11 students to be president and vice-president? Click here to see answer by Nate(3500)

 Question 85109: 2.Of 10 candidates, the first 6 are being interviewed in the morning, and the last 4 in the afternoon. In how many ways can the interviewer arrange a schedule? Click here to see answer by stanbon(57361)

 Question 85108: 1.How many different two-digit numbers can be formed from the digits 3, 1, 4, and 5 (allowing reuse)? Click here to see answer by stanbon(57361)

 Question 85114: How many seven-digit phone numbers can be formed if the first digit cannot be 0 and a)repetition of digits is not permitted? b)if repetition of digits is permitted? Click here to see answer by stanbon(57361)
 Question 85114: How many seven-digit phone numbers can be formed if the first digit cannot be 0 and a)repetition of digits is not permitted? b)if repetition of digits is permitted? Click here to see answer by Nate(3500)

 Question 85082: hey i need help with word probabilitiesfor example... the letters a through z are written on pieces of paper and placed in a jar. Four of them are selected one after the other without replacing any of them. and how do you know how to do it. Click here to see answer by stanbon(57361)

 Question 85120: The Board of Directors does not have assigned seats in the conference room. If there are 12 of them, seated at a round table, how many different seating arrangements are possible? Click here to see answer by stanbon(57361)

 Question 85123: Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if: the first letter must be Y the vowels and consonants alternate, beginning with a consonant (Y is a consonant here and Y does not have to be first Click here to see answer by jim_thompson5910(28595)

 Question 85233: State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery? Click here to see answer by stanbon(57361)

 Question 85232: A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses. How many ways can 4 toppings be selected where: a.All the toppings are vegetables b.All the toppings are meat c.There is only cheese on the pizza d.There are 2 vegetables, 1 meat and 1 cheese e.There are 3 meats and 1 cheese. Click here to see answer by stanbon(57361)

 Question 85230: I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls? Click here to see answer by stanbon(57361)

 Question 85229: I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected? Click here to see answer by stanbon(57361)

 Question 85182: State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery? Click here to see answer by scianci(186)

 Question 85180: I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls? Click here to see answer by scianci(186)

 Question 85179: I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected? Click here to see answer by scianci(186)

 Question 85468: Could you help me with this problem: Evaluate 20! Thanks! Click here to see answer by jim_thompson5910(28595)

 Question 85469: Please solve: 10 C 3 Thank you. * the 10 and 3 of course are ment to be sub numbers Click here to see answer by jim_thompson5910(28595)

 Question 85484: A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses. How many ways can 4 toppings be selected where: a.All the toppings are vegetables b.All the toppings are meat c.There is only cheese on the pizza d.There are 2 vegetables, 1 meat and 1 cheese e.There are 3 meats and 1 cheese. : A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses. How many ways can 4 toppings be selected where: a.All the toppings are vegetables b.All the toppings are meat c.There is only cheese on the pizza d.There are 2 vegetables, 1 meat and 1 cheese e.There are 3 meats and 1 cheese. Click here to see answer by checkley75(3666)

 Question 85795: How many three-digit numbers can you form from the digits 1, 2, 3, 4, 5, 6 if: a.) the digits can be repeated b.) The digits can not be repeated Click here to see answer by stanbon(57361)

 Question 85794: Could you please assist me in solving this question?: (3 points) Solve the following equation for n: nC2=100C98 Thank you, Gary Click here to see answer by stanbon(57361)

 Question 85849: Please throughly explain how to solve this problem: To win the Lotto in the state of Alabama, one must correctly select 6 numbers from a collection of 49 (1 through 49). This order in which the selection is made does not matter. How many different selections are possible? Thanks Click here to see answer by checkley75(3666)
 Question 85849: Please throughly explain how to solve this problem: To win the Lotto in the state of Alabama, one must correctly select 6 numbers from a collection of 49 (1 through 49). This order in which the selection is made does not matter. How many different selections are possible? Thanks Click here to see answer by Edwin McCravy(8909)

 Question 85850: Please help me find a solution to this problem Blue-Bunny Ice Cream, sells 31 flavors. A.) How many 2-dip cones are possible if order of flavors is to be considered and no flavor is repeated? B.) How many 2-dip cones are possible if order of flavors is to be considered and flavors CAN be repeated. C.) How many 2-dip cones are possible if order is NOT considered and NO flavor is repeated? Thanks Click here to see answer by Edwin McCravy(8909)

 Question 86701: Can you please assist me with this? In how many different orders can you arrange 4 vases on a bookcase self? Click here to see answer by stanbon(57361)

 Question 86700: May you help me in solving this problem? I'm afraid I don't even know what formula to use. I can't even find this section in my text book. Thanks! Use these figures for 1999 resident U.S. population by age to answer this question: AGE ------POPULATION (In Thousands) 0-19 ------75,791 20-39 ----81,004 40-59 ------62,383 75-84 -----11,145 85 and older ----3,628 A.) Find the Probability that the resident is under the age of 20. B.) Find the Probability that the resident is in the 20-39 or 60-74 age group. Click here to see answer by Flake(45)