Key idea: Vitamins are classified as:

• Fat-soluble: can be stored in the body
• Water-soluble: generally cannot be stored significantly in the body

List the given vitamins: $A,\, B_1,\, B_6,\, B_{12},\, C,\, D,\, E,\, K$

Identify which of these are stored in the body:

• $A$ : fat-soluble, so stored
• $B_1$ : water-soluble, so not stored
• $B_6$ : water-soluble, generally not counted as stored in this classification
• $B_{12}$ : though water-soluble, it is an exception and can be stored in the liver
• $C$ : water-soluble, not stored
• $D$ : fat-soluble, so stored
• $E$ : fat-soluble, so stored
• $K$ : fat-soluble, so stored

Count the stored vitamins: $A,\, B_{12},\, D,\, E,\, K$

Total number: $5$

Final answer: $\boxed{5}$

Comparison with stored correct answer: Stored correct answer = $5$

This matches our derived answer.