Question: 35 Numeric 6 points How many unique letter sequences (orderings) can you make from the letters of…

35 Numeric 6 points

How many unique letter sequences (orderings) can you make from the letters of the word: ASSESSMENT

Type your answer…

36 File Upload 0 points

Please submit all work here if you have not done so previously.

Solution

To determine how many unique letter sequences can be made from the word “ASSESSMENT,” we need to account for the repeated letters. 1. Count the total number of letters in “ASSESSMENT”: \[ 9 \] 2. Identify the frequency of each repeated letter: - S appears 3 times - E appears 2 times 3. Apply the permutation formula for repeated items: \[ \frac{9!}{3! \cdot 2!} \] 4. Calculate \(9!\): \[ 9! = 362880 \] 5. Calculate \(3!\): \[ 3! = 6 \] 6. Calculate \(2!\): \[ 2! = 2 \] 7. Divide by the factorials of the repeated letters: \[ \frac{362880}{6 \cdot 2} = \frac{362880}{12} = 30240 \] The number of unique sequences is 30240.