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 students
Number of ways = 22C7
= 22!/7!(22 − 7)!
= 22!/7!(15)! = 170544
All 3 don’t join
Remaining 10 chosen from 22 students
Number of ways = 22C10
= 22!/10!(22 − 10)!
= 22!/10!12! = 646646
Thus,
Total number of ways = 170544 + 646646
= 817190

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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