Sets and Relations
Complex Numbers 33
Sequences and Series
Locus and Straight Line
Measures of Dispersion
Bivariate Frequency Distribution and Chi Square Statistic
Permutations and Combinations
- Introduction of Permutations and Combinations
- Fundamental Principles of Counting
- Concept of Addition Principle
- Concept of Multiplication Principle
- Concept of Factorial Function
- Concept of Permutations
- Permutations When All Objects Are Distinct
- Permutations When Repetitions Are Allowed
- Permutations When All Objects Are Not Distinct
- Circular Permutations
- Properties of Permutations
- Concept of Combinations
- Properties of Combinations
- Properties of Permutations:
(i) nPn = n!
(ii) nP0 = 1
(iii) nP1 = n
(iv) nPr = n × (n - 1)P(r - 1)
= n(n -1) × (n - 2)P(r - 2)
= n(n - 1)(n - 2) × (n - 3)P(r - 3) and so on.
(v) `(np_r)/(np_(r - 1))= n - r + 1`.
Find the number of words that can be formed by using all the letters in the word REMAIN. If these words are written in the dictionary order, what will be the 40th word?
Find the number of ways of distributing n balls in n cells. What will be the number of ways if each cell must be occupied?
Thane is the 20th station from C.S.T. If a passenger can purchase a ticket from any station to any other station, how many different ticket must be available at the booking window?
Delegates from 24 countries participate in a round table discussion. Find the number of seating arrangements where two specified delegates are never together.
Five men, two women, and a child sit around a table. Find the number of arrangements where the child is seated between two men.
Eight men and six women sit around a table. How many of sitting arrangements will have no two women together?