# NCERT Class 11 Mathematics Solutions: Chapter 7 –Permutation and Combinations Miscellaneous Exercise Part 3

1. From a class of students, are to be chosen for an excursion party. There are 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?

From the class of students, are to be chosen for an excursion party.

Since there are 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.

So, the remaining students can be chosen from the remaining students in ways.

Case II: None of the three students join.

So, students can be chosen from the remaining students in ways.

So, required number of ways of choosing the excursion party is

2. In how many ways can the letters of the word be arranged so that all the S’s are together?

In the given word ASSASSINATION, the letter A appears 3 times, S appears 4 times, I appears 2 times, N appears 2 times, and all the other letters appear only once. Since all the words have to be arranged in such a way that all the SS are together, SSSS is treated as a single object for the time being. This single object together with the remaining 9 objects will account for 10 objects.

These 10 objects in which there are 3 As, 2 Is, and 2 Ns can be arranged in ways.

So, Required number of ways of arranging the letters of the given word