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[tex]\large \bold {ANSWER}[/tex]
[tex]\large \bold {SOLUTION}[/tex]
Well, the first thing we have to do is see if we have any repeated letters and count how many letters the word has.
The word has 10 letters, the letters "i" is repeated once. So we need to exclude the repetitions.
[tex]10 - 2 = 8[/tex]
Once this is done, we will use the combinatorial analysis, we will use this formula:
[tex]{C}^{p}_{n} = \frac{n!}{p!(n- p)!}[/tex]
The n is the number of letters and the o will be the number of elements we want to know how many groups are possible. Which will be the 4. The symbol of ! means factorial.
[tex]\begin{gathered}{C}^{4}_{8} = \frac{8!}{4!(8 - 4)!} \\ \\ {C}^{4}_{8} = \frac{8 \times 7 \times 6 \times 5 \times \not4 !}{4! \times \not4!} \\ \\ {C}^{4}_{10} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} \\ \\ {C}^{4}_{10} = \frac{1680}{24} = 70\end{gathered}[/tex]
