What value will come in place of question mark (?) in the number series given below ?
`"362880 45350 ? 1080 216"`

Options

A. 6380
B. 5880
C. 6480
D. 6280

Answer

To find the value that will replace the question mark (?) in the series "362880, 45350, ?, 1080, 216", we need to analyze the pattern in the series.

### Step-by-Step Solution:

1. **Identify the series**: The series given is 362880, 45350, ?, 1080, 216.

2. **Look for a pattern**: We will examine the relationship between the numbers in the series.

3. **Calculate the ratio between consecutive terms**:
- From 362880 to 45350:
\[ \frac{45350}{362880} \approx 0.1249 \quad (\text{This is approximately } \frac{1}{8}) \]
- From 45350 to ?:
- We will denote the unknown term as \( x \).
- From \( x \) to 1080:
\[ \frac{1080}{x} \]
- From 1080 to 216:
\[ \frac{216}{1080} = \frac{1}{5} \]

4. **Establish a pattern**:
- It seems that each term is being multiplied by a decreasing factor. The first term is multiplied by approximately \( \frac{1}{8} \), and then we need to find the factor for the unknown term \( x \).

5. **Calculate the unknown term**:
- Let's assume the pattern continues with a multiplication factor. If we take the factor from 1080 to 216, which is \( \frac{1}{5} \), we can assume that the factor from \( x \) to 1080 is \( \frac{1}{6} \).
- Thus, we can set up the equation:
\[ x \cdot \frac{1}{6} = 1080 \implies x = 1080 \cdot 6 = 6480 \]

6. **Final answer**:
- The value that will come in place of the question mark (?) is **6480**.