Question 3:- 2n chairs are arranged symmetrically around a table. there are 2n people including A and B, whose wish to occupy the chair. Find the number of seating arrangements if:-
(i) A and B are next to each
(ii) A and B are diametrical
Solution:- (i) If A and B sit together then, number of people = 2n – 2 + 1
= 2n – 1
Arrangement of (2n-1) people in circular arrangement = (2n – 2)!
Now the arrangement if AB and BA exist then = (2n-1)!×2!
= 2 × (2n-2)!
(ii) If A and B sit diametrical
A sit anywhere then B sit diametrical, hence number of people for arrangement in circle = (2n-1)
So, the number arrangement = (2n -2)!
Question 1:- Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from {A, B, C, D, E} or a number {1, 2, 3, 4, 5} with the repetition of characters allowed. If the number of passwords in S whose at least one character is a number from {1, 2, 3, 4, 5} is 
, then α is equal to
Solution:- See full solution
Question 2:- How many ways 6 Boys & 6 Girls batch students can be seated around a circular table such that no two boys are together.
Solution:- See full solution
Question 4:- Assuming cricket wordcup-2023 is played 10 teams. How many total matches are played in the league stage if each team plays with every other team exactly once
Solution:- See full solution
Question 5:- From a library containing 5 identical physics books, 4 identical chemistry books & 6 identical maths books. Find the number of ways in which we can select
(a) At least one book
(b) At least one book of each subject
(c) At least 2 books
(d) At least 2 book of each subject.
Solution:-See full solution
Question 6:- In a hotel four rooms are available Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons . Then the number of all possible ways in which this can be done is ______
Solution:- See full solution