Since you have told me that you are 12 you will not understand this but I will show you.
The number of ways that 4 books can be selected from 15 is
$$15C4 = \frac{15!}{4!11!}$$ on the calc this is $${\left({\frac{{\mathtt{15}}{!}}{{\mathtt{4}}{!}{\mathtt{\,\times\,}}({\mathtt{15}}{\mathtt{\,-\,}}{\mathtt{4}}){!}}}\right)} = {\mathtt{1\,365}}$$
The number of ways that 2 Lewis Carroll books can be chosen from the 5 is 5C2 = $${\left({\frac{{\mathtt{5}}{!}}{{\mathtt{2}}{!}{\mathtt{\,\times\,}}({\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{2}}){!}}}\right)} = {\mathtt{10}}$$
The number of ways the other 2 can be chosen from the other 10 books is 10C2 = $${\left({\frac{{\mathtt{10}}{!}}{{\mathtt{2}}{!}{\mathtt{\,\times\,}}({\mathtt{10}}{\mathtt{\,-\,}}{\mathtt{2}}){!}}}\right)} = {\mathtt{45}}$$
so the number of ways that the 2 Lewis Carroll books can be chosen is 45*10 = 450
The probability of choosing exactly 2 Lewis Carroll books is $${\frac{{\mathtt{450}}}{{\mathtt{1\,365}}}} = {\frac{{\mathtt{30}}}{{\mathtt{91}}}} = {\mathtt{0.329\: \!670\: \!329\: \!670\: \!329\: \!7}}$$
so the answer is $${\frac{{\mathtt{30}}}{{\mathtt{91}}}}$$
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