Several logs are stored in a pile with 18 logs on the bottom layer, 17 on the second layer, 16 on the third layer, and so on. If the top layer has one log, how many logs are in the pile? 170 171 162 153 none of the above

Q: Three Players were numbered as 1, 2, and 3. How many teams of two players can be formed? List down…

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Q: A bag contains 4 red, 6 white, and 9 blue marbles. How many ways can 5 marbles be selected to meet…

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Q: 52. There are 40 students in a summer cohort. Of those students, 20 are taking an accounting course,…

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Q: A student has five mathematics books four history books, and eight fiction books. In how many diff…

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A: The expression,nCr is evaluated using the formula, nCr=n!(n-r)!r! . The number of ways 1 person can…

Q: 10) There are 8 members on a board of directors. If they must form a subcommittee of 6 members, how…

A: Given data 8 members available  We have to select 6 from it for committee Here order of selection…

Q: A four digit number is to be formed from the digits 0, 2, 5, 7, 8. How many numbers can be formed if…

A: 4 ways to fill it (2,5,7,8) 5 ways to fill it (0,2,5,7,8) 5 ways to fill it (0,2,5,7,8) 5 ways to…

Q: How many numbers can be formed from the digits 1, 2, 3, and 4 if repetitions are not allowed?

A: How many numbers can be formed from the digits 1, 2, 3, and 4 if repetitions are not allowed.

Q: Six people are about to enter a cave in a single row. In how many ways could the arrange themselves…

A: Given: Six people are about to enter a cave in a single row

Q: At a certain university 523 of the seniors are history majors or math majors (or both). There are…

A: Given that 523 of the seniors in a certain university are history majors or math majors. Let H…

Q: 2. A clothing store wants to stock sweatshirts that come in four sizes (small, medium, large,…

A:

Q: Telephone poles are being stored in a pile with  25 poles in the first layer, 24 in the second, and…

A: Explanation: According to the question:  In a pile,  1st layer contains = 25 poles 2nd layer…

Q: A company is creating three new divisions, and seven managers are eligible to be appointed head of a…

A: No. of Managers = 7 No. of positions = 3

Q: A club with ten members is to choose three​ officers: ​ president, vice-president, and​…

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Q: At a music​ festival, there are ten bands scheduled to​ play, numbered 1 through 10. a. How many…

A: At a music​ festival, there are ten bands scheduled to​ play, numbered 1 through 10.   a. Number of…

Q: 1. How many different license plates are possible using 3 letters followed by 3 digits? digits and…

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Q: How many​ 10-digit telephone numbers​ (area code+​number) are possible if the first digit cannot be​…

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Q: Telephone poles are being stored in a pile with 25 poles in the first layer, 24 in the second 23 in…

A: Given that Telephone poles are being stored in a pile with 25 poles in the first layer, 24 in the…

Q: Five of ten books are arranged on a shelf. In how Many waYS Can this be done?

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Q: A large amphitheater is set up in such a way that there are 16 seats in the first row 27 seats in…

A: The given problem is regarding arithmetic progression series. First-term is given. A common…

Q: Six math books, four physics books and three chemistry books are arranged on a shelf. How many…

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Q: A clown owns 8 hat(s), 7 horn(s), 6 oufits. How many different outfits can the clown put together if…

A: Solution

Q: A club with eighteen members is to choose three officers: president, vice-president, and…

A: topic - permutations and combinations

Q: An office building has six doors. In how many ways can a person enter the building through a…

A: When a number of things are arranged in some order or a rearrangement is made for those things, this…

Q: Four digit numbers can be formed from the six digits 2, 3, 5, 6, 7, and 0. If repetitions are not…

A: here given , 4 digit number can be formed from the six digits 2,3,5,6,7 and 0 4 digit number can be…

Q: On a certain senate subcommittee there are five senators: Avi, Bonita, Chloe, Dean, and Ellen. Three…

A: We have to find the number of possible subcommittees.

Q: A certain Physics class is composed of 10 ECE, 15 CE and 20 ME students. In how many ways can a…

A: Given that  Total member=15 Total ECE=10  Total  CE=15 Total ME=20

Q: Each telephone number in a city consists of 7 digits, the first of which must be 3 or 4. (a) How…

A: HERE TELEPHONE Diary consists of 7 digits, first is either 3 or 4.

Q: An MLB team has 40 players, 25 of which are position players (only play a fielding position, and not…

A: Permutation is a technique to obtain the possible arrangements of listed items in linear order. It…

Q: A student may answer any six of ten questions on an examination. (a) In how many ways can six…

A: Given:  A student may answer any six of ten questions on an examination.To find:a)The number of ways…

Q: 3) A committee of 8 is to be selected from 18 Biologists and 10 Mathematicians. How many ways can…

A: Given 18=Biologist  10= Mathematics  Farmula used nCr=n!/(r!(n-r)!) r!=r(r-1)(r-2)...3.2.1

Q: A large pile of coins consists of pennies, nickels, dimes, and quarters (at least 20 of each). How…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: A. How many 3 digit numbers greater than 200 can be made from 0,1,2,3,4,5 if repetition of digits is…

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Q: 1. In a volleyball tournament, six teams take part and each team has to play every other team…

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Q: How many committed of 7 people can be formed from a pool of 30 people

A: we have to find no of ways committed of 7 people can be formed from a pool of  30 people

Q: Box A contained 225 pens. Box B contained 320 rulers, Some pens were moved from Box A to Box B and…

A: Given- Box A contained 225 pens. Box B contained 320 rulers. Some pens were moved from Box A to Box…

Q: A bag contains four red marbles, three green ones, one lavender one, three yellows, and three orange…

A: There are number of marbles in bag: Number of red marbles: 4 Number of green marbles: 3  Number of…

Q: A bag contains three red marbles, three green ones, one lavender one, two yellows, and three orange…

A: Solution: Given information: Red marbles = 3 Green marbles = 3  Lavender  marble = 1 Yellow marble =…

Q: There are 25 people in a club. In how many ways can the club elect a president, a secretary and a…

A:

Q: A license plate consists of two letters and three digits. How many different plates can be made if…

A: no.of digits (0 to 9)=10no.of letters (A to Z)=26

Q: How many different choices can be made from 5 red beads, 4 gold beads and 8 blue beads if at least…

A: As per our guidelines we are supposed to answer only one question per post so i am solving first…

Q: How many poles will there be in a stack of telephone poles if there are 58 in the first layer, 57 in…

A:

Q: A bag contains three red marbles, one green one, one lavender one, three yellows, and three orange…

A: Total number of marbles, n = 3 red + 1 green + 1 lavender + 3 yellow + 3 orange = 11 Number of red…

Q: 11 Given the digits 6, 7, 8, 9, a. How many four number digits can be formed if there's no…

A: Given digits are  6, 7, 8, 9 each parts are solved below.

Q: A certain country's postal service currently uses 5-digit zip codes in most areas. How many zip…

A: If No Restrictions on the digitSince country uses 5-digit codes and the digits are…

Q: How many ways are there to select an all-star team which includes all members from A, all members…

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Q: 2. In a certain country, license plate numbers have 3 letters followed by 3 digits. How many…

A: here use counting principle  for combination  nr = n!(n- r)! r!

Q: Consider a bag containing seven red marbles, two green ones, one transparent one, seven yellow ones,…

A: Determine the number of sets of five marbles include at most one of the red ones but no yellow ones.…

Q: A student has 20 video games: 4 adventure games, 6 arcade games, 5 puzzle games, and 5 simulation…

A: Given: Number of adventure games  = 4 Number of arcade games = 6 Number of puzzle games = 5 Number…