A) \[^{52}{{C}_{18}}^{35}{{C}_{2}}\]
B) \[^{52}{{C}_{18}}{{\times }^{35}}{{C}_{2}}{{+}^{52}}{{C}_{19}}{{\times }^{35}}{{C}_{1}}{{+}^{52}}{{C}_{20}}\]
C) \[^{52}{{C}_{18}}{{+}^{35}}{{C}_{2}}{{+}^{52}}{{C}_{19}}\]
D) \[^{52}{{C}_{18}}{{\times }^{35}}{{C}_{2}}{{+}^{35}}{{C}_{1}}{{\times }^{52}}{{C}_{19}}\]
Correct Answer: B
Solution :
[b] The following are the number of possible choices: \[^{52}{{C}_{18}}{{\times }^{35}}{{C}_{2}}\] (18 families having at most 2 children and 2 selected from other type of families) \[^{52}{{C}_{19}}{{\times }^{35}}{{C}_{1}}\](19 families having at most 2 children and 1 selected from other type of families) \[^{52}{{C}_{20}}\] (All selected 20 families having at most 2 children). Hence, the total number of possible choices is: \[{{=}^{52}}{{C}_{18}}{{\times }^{35}}{{C}_{2}}{{+}^{52}}{{C}_{19}}{{\times }^{35}}{{C}_{1}}{{+}^{52}}{{C}_{20}}\]
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