Find the number of arrangements of the digits {0,1,2,3,4,5,6,7,8,9} such that the first digit is less than 7 AND the second digit is greater than or equal to 2.

Q: How many ways are there to distribute eight balls into six distinct boxes with at least one ball in…

A: The balls are identical. In this case there are 8 balls and 6 boxes to be placed, so each box can be…

Q: A pencil case has 400 colored markers: 200 blue, 120 red, 50 green, and 30 yellow. What is the least…

A: Given problem Given that   A pencil case has 400 colored markers . 200 blue 120 red 50 green 30…

Q: List all the ordered arrangements of 4 objects 1, 2, 3, and 4 choosing 3 at a time without…

A: 4 objects are 1,2,3,4 If we have to choose 3 out of 4 (without repetition) Then, First object can be…

Q: Find the number of ways of placing 12 balls in a row given that 5 are red, 3 are green and 4 are…

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Q: Find the number of the permutation of 8 different things taken 3 at a time

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Q: Find all the mindir and colartors of matrin A. -2 3. A- 6. -1 -3 1.

A: The minor of all the elements of a matrix can be obtained by deleting the corresponding row and…

Q: (i) Determine how many rows are in the corner section of a stadium containing 3920 seats if the…

A: the total number of seats in the stadium are 3920  the first row has 10 seats,  The second row has…

Q: How many subsets does the set  F = {4, 5, 6, 7, 8}  have?

A: Given : F = 4, 5, 6, 7, 8

Q: Let [A1, A2], [B1, B2], [C1, C2] be 3 married couples who attended a concert.  In how many ways can…

A: Permutation: A permutation is an arrangement of objects in a definite order. Let n is the total…

Q: . Bricks are stacked in 20 rows such that each row has a fixed number of bricks more than the row…

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Q: Show that on a street with 101 houses where each house has a distinct street number between 1 and…

A: For the solution of the problem follow the next step.

Q: nd presently has 3 lots to build on

A: Given : a contractor builds homes of 6 different models and presently has 3 lots to build on.  we…

Q: A garderning company is planting trees and flowers at 3 sites on the median of a new road. For each…

A: * SOLUTION :-

Q: Use any method, list all the three digit numbers from the set {3,4,5,6} where there are no repeating…

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Q: How many ways are there to list the digits {1,2, 2, 3, 4, 5, 6} so that identical digits are not in…

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Q: from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 if repetition is not allowed and all the odd digits occur…

A: The biggest possible number is 975,318,642; the digit zero(0) is being excluded from the question…

Q: same

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Q: Suppose I choose two numbers from the set {1, 2, 3,... 100}. How many have an even sum? Show all…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find the number of permutations using four different numbers (2,5,11,30) if they are taken 2 at a…

A: Given that, Four different numbers are (2,5,11,30) To find: Number of permutations using four…

Q: A 6-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the…

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Q: How many ways are there to put 5 balls in 2 boxes if the balls are distinguishable and the boxes are…

A: Total number of distinct boxes=n=2 Total number of distinct balls=r=5

Q: How many pairs of two distinct integers chosen from the set {1, 2, 3,..., 101} have a sum that is…

A: Since you have posted multiple questions and we can answer one question. So answer provided for the…

Q: Suppose you must use 1x“-tile and 10 x-tiles. You only have up to 15 1-til use. How many of the…

A: Introduction: A rectangle is a quadrilateral with equal angles and opposite sides that are equal and…

Q: Show that if seven integers are selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, there must be…

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Q: Assume that you are assigning one of 12 available lockers to each of the 8 players on the team. In…

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Q: How

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Q: When I arrange the members of a marching band in rows of 2, 3, or 4, there is always 1 person left…

A: To solve the given problem

Q: Suppose that the number of students in a class increase by 2, the number of ways they may be…

A:

Q: Show that there are infinitely many examples of two consecutive positive integers that cannot be…

A: According to the given information, It is required to prove that there are infinitely many examples…

Q: How many subsets does the set  F = {3, 4, 5, 6, 7} have?

A: No. of subsets in a set: The number of subsets in a set containing n elements is given by 2n. No. of…

Q: Determine the number of ways such that 5 men and 5 women be seated at a round table if no two women…

A: No. of men = 5  No. of women = 5

Q: 2. Assume that you have lots of pennies and nickels and you start arranging them in rows of 8 coins.…

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Q: Suppose a n × n chessboard is missing two opposite corners. Prove that no matter what n is, you will…

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Q: If the mean of 5 positive integers is 15, what is the maximum possible difference between the…

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Q: Find the number of permutations x1, x2, x3, x4, x5,  of numbers 1, 2, 3, 4, 5 such that the sum of…

A: A number is divisible by 3 when one of the factors of the number is 3. Thus the sum…

Q: How many pairs of two distinct integers chosen from the set {1, 2, 3, 101} have a sum that is even?

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Q: How many different teams of 4 members can be selected from a pool of 20 applicants?

A: The combination formula is given by

Q: | Suppose 10 ducks and 6 geese line up in a single row. In how many ways can they line up so that no…

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Q: How many three-digit numbers is there such that when the middle digit is removed they become a…

A: Let the three digit number be xyz. then on removing the middle digit, the two digit number will…

Q: Find the number of ways that a committee of 7 members can be selected from 8 sociologists and 6…

A: Combination is a technique to obtain the possible arrangements of listed items, where the order of…

Q: If 8 subjects  are selected from the 12 that are available  and the 8 selected subjects are all…

A: Given that 8 subjects are selected from the 12 subjects. The selected 8 subjects are all treated at…

Q: A contractor builds homes of 9 different models and presently has 3 lots to build on. In how many…

A: We have to find no. Of ways..

Q: How many elements are in the set {0, {0}}?

A:

Q: Show that if any 14 numbers are selected from the set S = {1,2,3,...,25}, [14] there are at least…

A: Note that the numbers in each of the first twelve sets sum to 26, and that there is no pair of…

Q: From a garden with 6 flower varieties, a bouquet of 3 differer types of flowers is to be picked. How…

A: using permutation and combination in these type of problems.

Q: Let [A1, A2], [B1, B2], [C1, C2] be 3 married couples who attended a concert.  Show that the number…

A: Consider that G is the group of females and B is the group of males.This two group of G and B can be…

Q: Red and blue ceramic tiles are laid according to a pattern such that for every 22 red tiles used, 3…

A: Given that there are total 300 ties of Red and blue colour .according to pattern every 22 red…

Q: new employees, two of = that are lined up in a row.- -obability that the married

A: To find:  a. The probability that the married couple will have adjacent desks. b. The probability…

Q: assume that the 160 students who take this exam will receive one of 24 grades   i. What does the…

A: Given:-     assume that the 160 students who take this exam will receive one of 24 grades   i. What…

Q: A troop of 17 monkeys store their bananas in 11 piles of equal size, each containing more than 1…

A: To solve the given question first form system of congruences. then by appropriate method we will…