Question

From a class of 25 students, 10 are to be chosen for a project work. There are 3 students who decide that either all of them will join or none will join. In how many ways can they be chosen?

Answer 1

Answer:

²²C₇ + ²²C₁₀

Step-by-step explanation:

Hi,

Given a class of 25 students out of which 10 are to be chosen for a

project work.

The given scenario can be classified into following cases a follows:

Case 1:  Particular 3 students join together

Since already 3 students are joined , rest of the 7 should be selected

from remaining 22 students which could be done in ²²C₇ ways

Case 2: None of the 3 students will join

Since none of the 3 students will join , all of the 10 students should be

selected from remaining 22 students which could be done in

²²C₁₀ ways.

Hence, total number of ways students can be chosen for project

work are ²²C₇ + ²²C₁₀

Hope, it helps !