✒️[tex]\large{\mathcal{ANSWER}}[/tex]
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Well, the first thing we should do is see if we have any repeated letters and count how many letters the word has.
The word has 13 letters, the letters "i", "t", "n" and "e" are repeated, the letter "e" is repeated twice and the letters "i", "n" and "t" if repeat once each. So we need to exclude the repetitions.
[tex]13 - 2 - 1 - 1 - 1 = 8[/tex]
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Once that's done, we'll use combinatorial analysis, we'll use this formula:
[tex]c ^{p}_n = \frac{n!}{p!(n - p! )} [/tex]
One is the number of letters and o is the number of elements we want to know how many groups are possible. Which will be 4. The symbol for ! means factorial.
Substituted;
[tex]c^{4}_8 = \frac{8!}{4!(8 - 4)!} [/tex]
[tex]c^{4}_8 = \frac{8 \times 7 \times 6 \times 5 \times 4!}{4 !\times 4!} [/tex]
[tex] c^{4}_8 =\frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} [/tex]
[tex]c^{4}_8 = \frac{1680}{24} = 70[/tex]
[tex] \: \boxed{70} [/tex]
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