[tex] \large\underline \mathcal{{QUESTION:}}[/tex]
6. How many three-letter words can be formed from the letters of the word TUESDAY?
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[tex] \large\underline \mathcal{{SOLUTION:}}[/tex]
The word TUESDAY have 7 letters on it. Now , looking for the 3 lettered-words. We will use the permutation formula.
Given that: n=7 and r=3
[tex]\\[/tex]
[tex]\sf{P(n,r)=\frac{n!}{(n-r)!}}[/tex]
[tex]\sf{P(7,3)=\frac{7!}{(7-3)!}}[/tex]
[tex]\sf{P(7,3)=\frac{7!}{4!}}[/tex]
[tex]\sf{P(7,3)=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1}}[/tex]
[tex]\sf{P(7,3)=\frac{7 \times 6 \times 5 \times \cancel{4 \times 3 \times 2 \times 1}}{ \cancel{4 \times 3 \times 2 \times 1}}}[/tex]
[tex]\sf{P(7,3)=7\times6\times5}[/tex]
[tex]\sf{P(7,3)=210}[/tex]
[tex]\\[/tex]
[tex] \large\underline \mathcal{{ANSWER:}}[/tex]
[tex]\footnotesize\begin{aligned}\textsf{How many three-letter}\\\textsf{ words can be formed from}\\\textsf{ the letters of the word TUESDAY?} \\ \\ \sf \: P_r(n)=\frac{n!}{(n-r)!} \\ \\ \sf \: n = 7 \\ \sf \: r = 3 \\ \\ \sf \: P_3(7)=\frac{7!}{(7-3)!}=\frac{7!}{4!} \\ \\ \frac{7 \times 6 \times 5 \times \cancel{ 4 \times 3 \times 2 \times 1}}{ \cancel{4 \times 3 \times 2 \times 1}} = \boxed{ \sf \: 210 }\end{aligned}[/tex]
