Question

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?

Answer 1

`(8!)/(2! * 2!)`

Explanation:

Looking at the letters in DEADLINE,

it has a total number of 8 letters which could have been arranged 8! ways

if no letters were repeated.

But, we have letter 'D' and 'E' repeated twice, therefore both letters appeared 2! x 2! . other letters appears just once .

Hence to find the number of ways DEADLINE can be arranged, we have to divide the total number of ways DEADLINE could have been arranged without repetition by the number of appearance of each repeated letters

which is;
`(8!)/(2! * 2!)`

Answer 2

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

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.