The number of words (with or without meaning)
that can be formed from all the letters of the
word ``LETTER'' in which vowels never come
together is \_\_\_\_\_\_\_\_ .
Answer: 120
Solutions · 1
Official solution
LETTER: L,E,T,T,E,R --- E\times 2, T\times 2, L,R once each.
Arrange the non-vowel letters L,T,T,R: 2!4!=12 ways, creating 5 gaps. Place the 2 E's into 2 of these 5 gaps (no two E's in the same gap, so they're automatically not adjacent): (25)=10 ways.
\[\text{Total} = 12\times10 = 120\]