Given: 10 are chosen for an excursion party out of 25 students. There are 2 cases since 3 students decide either all or one of them will join.
Case 1: All the 3 students join. The remaining 7 students can be chosen out of 22 students in \(^{ 22} C_7\)ways.
Case 2: None of the 3 students join.
Thus, 10 students can be chosen in \( ^{ 22} C_{10}\) ways.
Hence, number of ways of choosing excursion party = \( ^{ 22} C_7+ ^{ 22} C_{10}\)
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