A library has $a$ copies of one book, $b$ copies each of two books, $c$ copies each of three books, a single copy of $d$ books. The total number of ways in which these books can be arranged in a shelf is equal to a. $\frac{\left(a+2b+3c+d\right)!}{a!{\left(b!\right)}^2{\left(c!\right)}^3}$ b. \displaystyle\frac{{{\left({a}+{2}{b}+{3}{c}+{d}\right)}!}}{{{a}!{\left({2}{b}!\right)}^{{{c}!}}^{3}}} c. $\frac{\left(a+b+3c+d\right)!}{{\left(c!\right)}^3}$ d. \displaystyle\frac{{{\left({a}+{2}{b}+{3}{c}+{d}\right)}!}}{{{a}!{\left({2}{b}!\right)}^{{{c}!}}^}}

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