Question

8 marks] In how many ways can the letters of the word "UNDERDOG" be arranged such that the first and last letters are same and no two vowels are together?​

Answer 1

The  letters of the word "UNDERDOG" can be arranged in 144 ways.

Number of ways "UNDERDOG"  can be arranged

There are only two letters that are the same which are D, then the remaining letters are 6 letters.

V, E, O are vowels

         N  R  G

The vowels are not joined together

For N, R, G  A³3

There are 4 openings A³4

Hence:

A³4· A³3=4×3×2×3×2×1

A³4· A³3=144

Therefore the  letters of the word "UNDERDOG" can be arranged in 144 ways.

Learn more about Number of ways "UNDERDOG"  can be arranged here:https://brainly.com/question/16088294

#SPJ1