In how many ways can 15 different books be di | vedclass

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(D) To divide $15$ different books into $3$ equal groups of $5$ books each,we first select $5$ books for the first group,then $5$ for the second,and t

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$126126$

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(D) To divide $15$ different books into $3$ equal groups of $5$ books each,we first select $5$ books for the first group,then $5$ for the second,and the remaining $5$ for the third.Number of ways to select the groups $= {}^{15}C_{5} 	imes {}^{10}C_{5} 	imes {}^{5}C_{5}$.Since the order of the $3$ groups does not matter,we divide by $3!$ to avoid overcounting.Required number of ways $= \frac{{}^{15}C_{5} 	imes {}^{10}C_{5} 	imes {}^{5}C_{5}}{3!} = \frac{3003 	imes 252 	imes 1}{6} = \frac{756756}{6} = 126126$.

In how many ways can $15$ different books be divided equally among $3$ sets or groups?

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