5 Questions
In how many ways can the six letters A, B, C, D, E and F be arranged in a row?
720 ways
If a job can be done in ‘m’ different ways, following which another can be done in ‘n’ different ways, how many total ways are there of doing the jobs?
m x n
The number of permutations of n objects, where p objects are of the same kind and rest are all different is?
n! / p!
In how many ways can six boys and four girls be arranged in a line?
3628800 ways
What is the formula for the number of permutations of n distinct objects?
n Pn = P ( n, n ) = n! = n ( n − 1) ( n − 2 ) 3 2 1
Study Notes
Permutations
- The number of ways to arrange 6 distinct objects (A, B, C, D, E, and F) in a row is a permutation problem.
- If a job can be done in 'm' different ways, and another job can be done in 'n' different ways, the total number of ways to do the jobs is the product of 'm' and 'n' (m × n).
Permutations of Objects with Duplicates
- The number of permutations of 'n' objects, where 'p' objects are of the same kind and the rest are different, can be calculated using a specific formula.
Permutations of Distinct Objects
- The formula for the number of permutations of 'n' distinct objects is n! (n factorial).
Real-World Applications
- The number of ways to arrange 6 boys and 4 girls in a line is a permutation problem.
Learn about permutations of distinct objects and understand how to calculate the number of arrangements using the formula n Pn = n! = n (n − 1) (n − 2 ) 3 2 1. Explore the Multiplication Principle and its application in determining the number of ways a job can be done.
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