Misc 10 - From a class of 25 students, 10 are chosen for excursion - Miscellaneous

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Misc 10 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? There are 2 options All 3 join Remaining 7 to be chosen from 25 – 3 =22 people Number of ways = 22C7 = 22!/7!(22 − 7)! = 22!/7!(15)! = 170544 Total number of ways = 170544 + 646646 = 817190

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