Permutation calculator is the number of ways of selecting ‘r’ objects from ‘n’ objects where different order of objects considered as different outcome.
It is represented as nPr in mathematical form.
Formula: nPr = n! / (n – r)!
Combination calculator is the number of ways of selecting ‘r’ objects from ‘n’ objects where order of objects selected is ignored or does not matter.
It is represented as nCr in mathematical form.
Formula: nCr = n! / [r!* (n – r)!]
Example 1: in how many 4-digit numbers can be formed using digits 4, 8, 3, 2, 5, 1 with no repetition of digits allowed?
Solution: since here we have to form a 4-digit number without repetition, and different order of digits forms different numbers we have to find permutation.
There are 6 digits available out of which we have to pick 4.
Hence n = 6 and r = 4.
6P4 = 6! / (6 – 4)! = 6! / 2! = 720/2 = 360
We can form 360 such numbers.
Example 2: in how many ways we can select a committee of 4 people among the group pf 10 people.
Solution: here have to form a committee of 4 people. While choosing a person it is we do not consider an order of who is selected first and then the second. Hence we use combination here.
We are going to select 4 people between 10.
10C4 = 10! / [4!* (10 – 4)!] = 210
Let x=-1; 1+1=-4A+2B+6; 2A–B=2; Let x=2 à 4+1=2A+2B+3; 1=A+B
Answer : A=1, C=2, D=-1
1/(x-1) + 2/(x-1)3 – 1/x