From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

Asked by Abhisek | 1 year ago |  162

##### Solution :-

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 = $$^{ 22} C_7+ ^{ 22} C_{10}$$

Answered by Pragya Singh | 1 year ago

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