Question

An almirah contains six different compartments.In how many ways can 12 identical books can be placed in compartment such that no compartment remains empty.​

Answer 1

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We need to Find the number of ways in which the books would be kept in the compartment

$\huge\star{\tt{\underline{\underline{\red{Answer}}}}}\star$

We need to give atleast one to each compartment

so,

we will keep one book each in the each compartment.

Let compartment be ${x}_{1}$,${x}_{2}$,${x}_{3}$,${x}_{4}$,${x}_{5}$${x}_{6}$=12

These all will have one book each so we will be left with onky 6 books

Therefore,

$\implies$$\large{\boxed{\blue{\tt{Formula ^{n+r-1-r}C_{r-1}}}}}$

${\boxed{n=12}}$

${\boxed{r=6}}$

$\implies$ $^{12+6-1-6}C_{6-1}$

$\implies$$^{11}C_{5}$

$\huge{\boxed{\boxed{462}}}$

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