Find the number of ways to arrange the letters in REFERENCE.
There are ways to arrange the letters in REFERENCE.

Question

Find the number of ways to arrange the letters in REFERENCE. There are $$ \square $$ ways to arrange the letters in REFERENCE.

UpStudy AI · Accepted Answer

Let the total number of letters in **REFERENCE** be $$ n = 9 $$. The frequency of each letter is as follows:
- **R** appears $$ 2 $$ times.
- **E** appears $$ 4 $$ times.
- **F**, **N**, and **C** each appear $$ 1 $$ time.

The formula for the number of arrangements is given by

$$
\frac{n!}{(2!)(4!)(1!)(1!)(1!)} = \frac{9!}{2! \cdot 4!}.
$$

Now, calculate each part:

1. Evaluate $$ 9! $$:
   $$
   9! = 362880.
   $$
2. Evaluate $$ 2! $$ and $$ 4! $$:
   $$
   2! = 2 \quad \text{and} \quad 4! = 24.
   $$
3. Compute the denominator:
   $$
   2! \cdot 4! = 2 \times 24 = 48.
   $$
4. Divide to find the number of arrangements:
   $$
   \frac{9!}{2! \cdot 4!} = \frac{362880}{48} = 7560.
   $$

There are $$ \boxed{7560} $$ ways to arrange the letters in **REFERENCE**.
There are 7,560 ways to arrange the letters in REFERENCE.

Find the number of ways to arrange the letters in REFERENCE.
There are ways to arrange the letters in REFERENCE.

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Find the number of ways to arrange the letters in REFERENCE. There are ways to arrange the letters in REFERENCE.

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Find the number of ways to arrange the letters in REFERENCE.
There are ways to arrange the letters in REFERENCE.