Answer to Question #146449 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, Y and Z follow one another?
a.36
b.48
c.24
d.12

Answer 1

If X, Y and Z follow one another, then the number of ways is:

$P = 3!*3! = 36.$

3! is for permutations of X, Y and Z, and 3! is for permutations of (X, Y, Z) and other two letters.

So, the correct answer is a. 36.