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N atoms are arranged to lie on a simple cubic crystal lattice. Then

M of these atoms are moved from their lattice sites to lie at the

interstices of the lattice, that is points which lie centrally between the

lattice sites. Assume that the atoms are placed in the interstices in a

way which is completely independent of the positions of the vacancies.

Show that the number of ways of taking M atoms from lattice sites

and placing them on interstices is W = (N!/M!(N − M)!)2 if there

are N interstitial sites where displaced atoms can sit.

I literally do not know where to start with this question I know W is the number of ways of choosing M atoms from N atoms but I don't really know where to go with this.

Help would be great.

Thanks :)

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# Homework Help: The number of ways of placing M atoms on the interstices of a lattice

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