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(C) The dehydration of alcohol $A$ ($3,4,4$-trimethylpentan-$2$-ol) in the presence of $H^+$ and heat proceeds via the formation of a carbocation. Fir

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$5$

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(C) The dehydration of alcohol $A$ ($3,4,4$-trimethylpentan-$2$-ol) in the presence of $H^+$ and heat proceeds via the formation of a carbocation. First,the secondary carbocation is formed,which undergoes a $1,2$-hydride shift to form a more stable tertiary carbocation. This tertiary carbocation can further rearrange via a $1,2$-methyl shift to form another tertiary carbocation. From these tertiary carbocations,elimination reactions occur to form alkenes. $1$. From the first tertiary carbocation,two alkenes are formed: $2,3,3$-trimethylpent-$1$-ene and $2,3,3$-trimethylpent-$2$-ene. $2$. From the second tertiary carbocation,two more alkenes are formed: $3,4,4$-trimethylpent-$1$-ene (which is chiral,giving a pair of enantiomers) and $3,4,4$-trimethylpent-$2$-ene. Counting the distinct products,including the enantiomeric pair,the total number of possible products is $5$.

For the given reaction,the total number of possible products formed by the tertiary carbocation of $A$ is $.........$.

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