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:- Number of Physics book = 5
Number of Chemistry book = 4
Number of maths book = 6
(a) Number of ways of selecting books = (5+1)×(4+1)×(6+1)
= 6×5×7 = 210
Number of ways of selecting at least one identical book = 210 -1 = 209
(b) Number of ways of selecting at least one book of each subject = 5×4×6
= 120
(c) Number of ways of selecting books = (5+1)×(4+1)×(6+1)
= 6×5×7 = 210
Number of ways of selecting no book = 1
Number of ways of selecting one book = 1 + 1 + 1 = 3
Hence, Number of ways of at least two book = 210 – 3 – 1 = 206
(d) Number of ways of selecting at least two book of each subject
=(5 – 1)(4 – 1)(6 – 1)
= 60
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 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:- 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 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