needing help with finding a solution to grade 6 math question from math makes sense homework book

Question: A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Chemistry Part II, unless Part I is also borrowed. In how many ways can he choose the three books to be borrowed? Answer: There are two ..

= (14 - 12) - (7 - 3) + (4 - 2) = 2 - 4 + 2 = 0 The system may have infinite number of solutions or no solution. Put x = k in (1) and (2) and solve y + z = 6 - k 2y + 3z = 14 - k. Solving the above two equations, we have z = k + 2 and y = 4 - 2k When x = k, subs..

We recall from our earlier classes that a system of linear equation with two variables is given by This system of linear equation may have either one solution or infinitely many solutions or no solution..

Question: Convert the following into factorials: i) 5.6.7.8.9.10 ii) 4.6.8.10.12 Answer: i) ii) ..

Question: At an election, three wards of a town are canvassed by 4, 5 and 8 men respectively. If 20 men volunteer, in how many ways can they be allotted to the different wards? Answer: Let the three wards be labelled as A, B and C respectively. Let us select 4 men for ward A. ..

Question: From 12 books, in how many ways can 5 be chosen i. to surely include a particular book ii. never to include a particular book iii. to have no restrictions at all? Answer: i. To include a particular book, one particular boo..

A system of linear equations is said to be consistent if it has a solution. This means that the solution satisfies all the equations in the system simultaneously. If a system of linear equations has no solution, then it is said to be inconsiste..

If D = 0 and all D 1 , D 2 and D 3 are zeros, this system has either infinite solution or no solution. In this case, put x = k(y = k or z = k), in any two of the equations, find y and z in terms of k. Substitute these values of x, y and z in terms of k, in the third..

There are 8 ways of travelling from A to B and seven ways for the return journey, since he cannot come by the same car. Hence, the number of ways of making both the journeys is 8 x 7 = 5..

Question: How many words of different 4 letters can be formed out of 7 capital letters, 3 vowels and 8 consonants, if each word starts with a capital letter and contains at least one vowel? Answer: Any capital letter can be chosen as the first letter of each word. So there are..