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Home » Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together.
CBSE | Class 11 | Maths | NCERT Exemplar | Permutations and Combinations
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together.

Solution:

It is known that,

=\frac{{ }^{n} P_{r}}{(n-r) !}

As per the question,

3 = Total number of vowels letter,

5 = Total number of consonants letter

    \[\begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline $\mathrm{T}$ & $\mathrm{R}$ & $\mathrm{I}$ & $\mathrm{A}$ & $\mathrm{N}$ & $\mathrm{G}$ & $\mathrm{L}$ & $\mathrm{E}$ \\ \hline \end{tabular}\]

Vowels can be placed in

{ }^{6} \mathrm{P}_{3}=6 ! / 3 !=120

5 !=120 = The number of way consonants can be arranged placed

As a result, the total number of ways it can be arranged

=5 ! \times^{6} P_{3}=120 \times 120=14400

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