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

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.