There are 18 rats and 3 cages. The rats have to be placed in all cages equally. In how many ways can the rats be placed?

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Solution

$As in each equal number of rats tobe placed, so 6 rats are placed in each cage . Number of ways in which rats can be placed = {}^{18}c_{6} \times {}^{12}c_{6} \times {}^{6}c_{6} = \frac{18!}{6! (18 - 6)!} \times \frac{12!}{6! (12 - 6)!} \times 1 = \frac{18!}{6! \times 12!} \times \frac{12!}{6! \times 6!} = \frac{18!}{6! \times 6! \times 6!} ways . ANS . . .$

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There are 18 rats and 3 cages. The rats have to be placed in all cages equally. In how many ways can the rats be placed?

As in each equal number of rats tobe placed , so 6 rats are placed in each cage.Number of ways in which rats can be placed =c618×c612×c66=18!6!18-6!×12!6!12-6!×1=18!6! × 12!×12!6! × 6!=18!6!×6!×6! ways. ANS...