Question:
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
Solution:
LETTER
vowels $=\mathrm{EE}$, consonant $=\mathrm{LTTR}$
$_{-} L_{-} T_{-} T_{-} R_{-}$
$\frac{4 !}{2 !} \times{ }^{5} \mathrm{C}_{2} \times \frac{2 !}{2 !}=12 \times 10=120$