The number of words

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__________.


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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