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

Question #146448
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
1
Expert's answer
2020-11-29T15:52:41-0500

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



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