a library shelf contains 7 books. in how many ways can they be arranged if there are no restrictions?

b. the mathamatics text book must be first.
c.the 3 math text boooks must be together

2 answers

a) 7!

b) 1 x 6!

c) treat the 3 math books as one item, pretend they are bundled together, so there are 5 items to arrange.
for 5! ways.
c)3! x 6!

The three must remain together but can be in any permutation with the rest. It would be 5! ways if the three books had to be in a certain position.