There are 4 letters and 5 boxes in a row. Number of ways of posting these letters if all the letters are not posted in the same box is

Options

A. 600
B. 620
C. 630
D. 700

Answer

To solve the problem of posting 4 letters into 5 boxes such that not all letters are posted in the same box, we can follow these steps:

### Step 1: Calculate total arrangements without restrictions
Each letter can be placed in any of the 5 boxes. Therefore, for 4 letters, the total number of ways to post them is given by:

\[ \text{Total ways} = 5^4 \]

Calculating this gives:

\[ 5^4 = 625 \]

### Step 2: Calculate the arrangements where all letters are in the same box
Next, we need to account for the restriction that not all letters can be in the same box. If all letters are in the same box, there are 5 possible scenarios (one for each box). Thus, the number of ways in which all letters are in the same box is:

\[ \text{Ways with all letters in one box} = 5 \]

### Step 3: Subtract the restricted arrangements from the total arrangements
To find the number of ways to post the letters such that not all letters are in the same box, we subtract the cases where all letters are in the same box from the total arrangements calculated in Step 1:

\[ \text{Required ways} = 5^4 - 5 \]

Substituting the values we calculated:

\[ \text{Required ways} = 625 - 5 = 620 \]

### Final Answer
Thus, the number of ways to post the letters such that not all letters are in the same box is:

\[ \boxed{620} \]