Problem $7.$ Consider a snippet of DNA which is coded by a sequence of nucleobase. There are four possible nucleobases: adenine $($A$),$ cytosine $($C$),$ guanine $($G$),$ thymine $($T$).$ For example, a snippet of DNA could look like "ACGCTAC".

$($a$)$ How many possible different DNA snippets that consist of $10$ nucleobases?

$($b$)$ If among the $10$ nucleobases, $4$ bases must be A$,3$ bases must G$,2$ bases must be C$,$ how many possible different $10-$base snippets that meet this condition?

$($c$)$ If among the $10$ nucleobases, $4$ bases must be $A,3$ bases must $G,$ how many possible different $10-$base snippets that meet this condition?

$($d$)$ Consider a DNA snippet of $10$ nucleobases: ACGTACGTAC.

a$.$ If only one nucleobase is mutated $($assuming it can mutate to any other nucleobase$),$ how many different mutations are possible from this snippet?

b$.$ If $3$ nucleobases are mutated, how many different mutations are possible?