555**7**56**7**56**77**5**77**5565556

There are a total of six 7's in the given number. But we need to determine the number of 7's that satisfy the condition that the **7 is preceded by 6 but NOT followed by 5.**

Starting from the left, let's try to check the number before and after 7.

_ _ 57*5_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ *

>The **7** here is preceded by * 5* and followed by

*5*, so this does not satisfy the condition above.

_ _ _ **_ **_*6*7*5 *_ **_ _ **_ **_ _ **_ _ _ _ _ _ _

> The **7** is preceded by * 6* and followed by

*5*. Still, this does not satisfy the given condition.

_ _ _ **_ **_ _ **_ **_ **67**7_ _ _ _ _ _ _ _ _ _

> The **7** is preceded by ** 6** and followed by

*7*. Hence this satisfy the condition the number before7should be 6 and after it ,should not be 5.

_ _ _ **_ **_ _ **_ **_ _ **_ _ **_*7*7*5*_ _ _ _ _ _

> The 7 is preceded by ** *** 7 and * by 5. Again, this does not satisfy the above condition.

**Hence, the number of 7's that is preceded by 6 and not followed by 5 is one only.**

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