A tertiary butyl carbocation is more stable than a secondary butyl carbocation because of which of the following?

A tertiary butyl carbocation has $9$ $\alpha$ -hydrogens available for hyperconjugation, whereas a secondary butyl carbocation has only $5$ $\alpha$ -hydrogens. Increased hyperconjugation and the $+I$ effect of three methyl groups stabilize the $3^{\circ }$ carbocation more effectively. Hyperconjugation is the primary electronic reason cited in the options.