question_answer

In a small village, there are 87 families, of which 52 families have at most 2 children. In a rural development program 20 families are to be chosen for assistance, of which at least 18 families must have at most 2 children. how many ways can the choice be made?                                                           

A) \[^{52}{{C}_{19}}{{\times }^{35}}{{C}_{1}}{{+}^{50}}{{C}_{19}}{{\times }^{37}}{{C}_{1}}{{+}^{52}}{{C}_{20}}\]

B) \[^{52}{{C}_{18}}{{\times }^{35}}{{C}_{2}}{{+}^{52}}{{C}_{19}}{{\times }^{35}}{{C}_{1}}{{+}^{52}}{{C}_{20}}\]

C) \[^{52}{{C}_{19}}{{\times }^{35}}{{C}_{1}}{{+}^{52}}{{C}_{19}}{{\times }^{35}}{{C}_{1}}{{-}^{52}}{{C}_{20}}\]

D) \[^{52}{{C}_{18}}{{\times }^{35}}{{C}_{2}}{{-}^{52}}{{C}_{19}}{{\times }^{35}}{{C}_{1}}{{+}^{52}}{{C}_{20}}\]

E) None of these