Answers are grounded in this paper and cite their sources.
Mantel, N. and Pasternack, B. (1968), A class of occupancy problems. The American Statistician, 22 (2): 23-24. 2. Takacs, L. (1967), On the method of inclusion and exclusion. J. Amer. Statis. Assoc., 62(317): 102-113. 3. Riordan, J. (1959), An Introduction to Combinatorial Analysis. John Wiley and Sons, New York. 4. Barton, D. E. and David, F. N. (1959), Contagious occupancy. J. Royal Statis. Soc., (B) 21(1): 120-133.
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D. A. Sprott (1969) studied this question.
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