How many different words can be formed with letters of the word SUNDAY ? How many of the words begin with N? How many begin with N and end Y?

Answer

To solve the problem step by step, we will break it down into three parts as per the question.

### Step 1: Calculate the total number of different words that can be formed with the letters of the word "SUNDAY".

The word "SUNDAY" has 6 distinct letters: S, U, N, D, A, Y.

To find the total number of different arrangements (or permutations) of these letters, we use the factorial of the number of letters.

\[ \text{Total arrangements} = 6! = 720 \]

### Step 2: Calculate how many of the words begin with N.

If we want to find the number of arrangements that begin with the letter N, we can fix N in the first position. This leaves us with the remaining letters: S, U, D, A, Y (5 letters).

The number of arrangements of these 5 letters is:

\[ \text{Arrangements starting with N} = 5! = 120 \]

### Step 3: Calculate how many words begin with N and end with Y.

If we want the arrangements that begin with N and end with Y, we can fix N in the first position and Y in the last position. This leaves us with the letters S, U, D, A (4 letters).

The number of arrangements of these 4 letters is:

\[ \text{Arrangements starting with N and ending with Y} = 4! = 24 \]

### Final Answers:
1. Total different words that can be formed: **720**
2. Words that begin with N: **120**
3. Words that begin with N and end with Y: **24**

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