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:

We know that the number of ways of selecting r different things from n different things is a combination and is calculated using the formula ⁿCᵣ = n! / [r!(n−r)!].

Case I - If the 3 students join the party, then the combination will be = ²²C₇ = 170544

Case II - If the 3 students do not join the party, then the combination will be = ²²C₁₀ = 646646

The number of ways that the excursion party can be chosen as = 170544 + 646646 = 817190

NCERT Solutions Class 11 Maths Chapter 7 Exercise ME Question 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?

Summary:

The number of ways that the excursion party can be chosen is 817190