Which formula can be used to determine the total number of different eight-letter arrangements that can be formed using the letters in the word DEADLINE?

The formula that can be used is 8!/2!2! which is equivalent to 10,080 ways

Step-by-step explanation:

Given the word DEADLINE, the letters in the word can be rearranged or formed in a number of ways using concept of permutation (since it deals with arrangement of numbers).

Since there are 8 letters in the word and two of the letters (D and E) are both repeated twice, then the word can be arranged in 8!/2!2! number of ways.

8!/2!2! = 8×7×6×5×4×3×2×1/2×1×2×1

8!/2!2 = 8×7×6×5×3×2

8!/2!2 = 10,080 ways

Note that 2! was repeated twice at the denominator because the letters D and E are both repeated twice.

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