The number of words
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:

For vowels not together

Number of ways to arrange $\mathrm{L}, \mathrm{T}, \mathrm{T}, \mathrm{R}=\frac{4 !}{2 !}$

Then put both $\mathrm{E}$ in 5 gaps formed in ${ }^{5} C_{2}$ ways.

$\therefore$ No. of ways $=\frac{4 !}{2 !} \cdot{ }^{5} C_{2}=120$

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