6.1 1 a) and b) let x be a string of length n, and let y be a string of length n − k, for 1 ≤ k < n. we wish to line up the symbols in x with the symbols in y by adding k blanks to y. a) suppose that we decide to add the k blanks in one continuous block. how many ways are there to do this? b) suppose that we add two separate blocks of blanks, one of size i and one of size k − i, for 1 ≤ i < k. how many ways are there to do this?

Ican interpret and represent the remainder in division calculations sensibly for the context (eg if we wont to know how many 40 seat buses will be needed to transport 170 students for on excursion, we divide 170 by 40 and realise buses and another smaller vehicle to that we need 4 transport 10 more students) solve the following questions. show your work! 11) the zoo had 420 butterflies that needed to be transported to a new enclosure. the boxes that the butterflies would be moved in only hold 80 butterflies in each. how many boxes would they need? 2 12) each classroom in the school can have exactly 25 students, if there are 345 students in the school how many full classrooms are there?