The are `8` events that can be schedules in a week, then
The total number of ways that these `8` event are scheduled on exactly `6` days of a week is

Options

A. `210xx6!`
B. `7!xx266`
C. `56xx7!`
D. `210xx7!`

Explanation

To solve the problem of scheduling 8 events on exactly 6 days of a week, we can break down the solution into clear steps.

### Step-by-Step Solution:

1. **Choose 6 Days from 7 Days**:
We need to select 6 days out of the 7 days in a week. The number of ways to choose 6 days from 7 can be calculated using the combination formula:
\[ \text{Number of ways} = \binom{7}{6} = 7 \]

2. **Distribute 8 Events Across 6 Days**:
We need to consider how to distribute 8 events over the 6 chosen days. There are two main cases to consider for distributing the events.

**Case 1**: 4 days have 1 event each, and 2 days have 2 events each.
- Choose 2 days from the 6 days to have 2 events each:
\[ \text{Ways to choose 2 days} = \binom{6}{2} = 15 \]
- The remaining 4 days will each have 1 event.
- The total arrangements of the 8 events (considering the indistinguishability of events on the same day):
\[ \text{Arrangements} = \frac{8!}{2! \times 2!} = \frac{40320}{4} = 10080 \]
- Therefore, the total for Case 1 is:
\[ \text{Total for Case 1} = 15 \times 10080 = 151200 \]

**Case 2**: 5 days have 1 event each, and 1 day has 3 events.
- Choose 1 day from the 6 days to have 3 events:
\[ \text{Ways to choose 1 day} = \binom{6}{1} = 6 \]
- The remaining 5 days will each have 1 event.
- The total arrangements of the 8 events (considering the indistinguishability of events on the same day):
\[ \text{Arrangements} = \frac{8!}{3!} = \frac{40320}{6} = 6720 \]
- Therefore, the total for Case 2 is:
\[ \text{Total for Case 2} = 6 \times 6720 = 40320 \]

3. **Combine Both Cases**:
Now, we sum the totals from both cases:
\[ \text{Total arrangements} = 151200 + 40320 = 191520 \]

4. **Multiply by the Ways to Choose Days**:
Finally, we multiply the total arrangements by the number of ways to choose the 6 days:
\[ \text{Final Total} = 7 \times 191520 = 1340640 \]

### Final Answer:
The total number of ways to schedule the 8 events on exactly 6 days of a week is **1340640**.