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 ?
Answer:
Total number of students = 25
Total students chosen for an excursion party = 10
If all the 3 students join the excursion party. So they are sure and for remaining 22 students, we have to select 7 students
Then total number of combinations = 22C7
Again if all 3 students do not join the excursion party. So for remaining 22 students, we have to select 10 students.
Then total number of combinations = 22C10
Now Total number of ways = 22C7 + 22C10
= 22!/(7! * 15!) + 22!/(10! * 12!)
= {(22*21*20*19*18*17*16*15!)/(7*6*5*4*3*2*15!)} + {(22*21*20*19*18*17*16*15*14*13*12)/(10*9*8*7*6*5*4*3*2*12!)}
= 817190
So total number of ways, the excursion party can be chosen = 817190
Not what you are looking for? Go ahead and submit the question, we will get back to you.
