The number of words (with or without meaning)

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 $=\mathrm{LTTR}$

$_{-} L_{-} T_{-} T_{-} R_{-}$

$\frac{4 !}{2 !} \times{ }^{5} \mathrm{C}_{2} \times \frac{2 !}{2 !}=12 \times 10=120$

 

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