Answer to Question #146448 in Combinatorics | Number Theory for Josh

Question

The letters V, W, X, Y and Z are selected at random to form a five letters word without repetition. How many ways can a word be formed such that X and Y follow each?
a.60
b.48
c.12
d.24

Answer 1

Let's observe one pair X and Y as one object. Now we have 4 objects. The number of permutations of 4 objects is

$$4!=24$$

The number of permutations of 2 letters in pair X and Y is

$$2!=2\ \ (XY\ \ or\ \ \ YX)$$

How many ways can a word be formed such that X and Y follow each?

$$4!\times 2!=24\times2=48$$

b. 48