[tex] \large\underline \mathcal{{QUESTION:}}[/tex]
how many 3 letter words can be made from the letters of the word triangle if repetition is not allowed?
[tex]\\[/tex]
[tex] \large\underline \mathcal{{SOLUTION:}}[/tex]
The word triangle have 8 letters on it. Now , looking for the 3 lettered-words. We will use the permutation formula.
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[tex]\sf{P(n,r)=\frac{n!}{(n-r)!}}[/tex]
[tex]\sf{P(8,3)=\frac{8!}{(8-3)!}}[/tex]
[tex]\sf{P(8,3)=\frac{8!}{5!}}[/tex]
[tex]\sf{P(8,3)=\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1}}[/tex]
[tex]\sf{P(8,3)=\frac{8 \times 7 \times 6 \times \cancel{5 \times 4 \times 3 \times 2 \times 1}}{ \cancel{5 \times 4 \times 3 \times 2 \times 1}}}[/tex]
[tex]\sf{P(8,3)=8\times7\times6}[/tex]
[tex]\sf{P(8,3)=336}[/tex]
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[tex] \large\underline \mathcal{{ANSWER:}}[/tex]
