Question:
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?
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?
Updated On: Oct 21, 2023
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Solution and Explanation
From the class of 25 students, 10 are to be chosen for an excursion party.
Since there are 3 students who decide that either all of them will join or none of them will join, there are two cases.
Case I: All the three students join.
Then, the remaining 7 students can be chosen from the remaining 22 students in \(^{22}C_7\) ways.
Case II: None of the three students join.
Then, 10 students can be chosen from the remaining 22 students in \(^{22}C_{10}\) ways.
Thus, required number of ways of choosing the excursion party is \(^{22}C_7+^{22}C_{10}.\)
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