The number of ways can a collection of 30 books be divided into two groups of 10 and 20 so that the first group always contains a particular book is

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$^{29} C_{29}$

$^{29} C_{10}$

$^{29} C_{20}$

$^{29} C_{9} \times^{29} C_{20}$

answer is B.

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Detailed Solution

The particular book is kept in first group in one way.

The remaining 29 things to be divided into two groups containing19 and 10 Required no. of ways $= {\frac{29!}{10! 19!} = 29_{C}}_{9} = {29_{C}}_{20}$ .

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