# From a class of 25 students, 10 are to be chosen for an excursion party.

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?

Solution:

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 ${ }^{22} \mathrm{C}_{7}$ ways.

Case II: None of the three students join.

Then, 10 students can be chosen from the remaining 22 students in ${ }^{22} \mathrm{C}_{10}$ ways.

Thus, required number of ways of choosing the excursion party is ${ }^{22} \mathrm{C}_{7}+{ }^{22} \mathrm{C}_{10}$.