A permutation is an arrangement, or listing of objects in which order is important.
COMBINATION
A COMBINATION is an arrangement of objects in which order is not important.c
nCr = n!/(n-r)!r!
nPr = n!/(n-r)!
: The number of distinct PERMUTATIONS of n objects is “n factorial”, denoted by n! = 1 × 2 × 3 × ... × n, or equivalently, = n × (n − 1) × (n − 2) × ... × 2 × 1
RULE 1 If n is a positive integer, then the number of permutations or rearrangements of a set of n objects in a row is n!. Repetition is not allowed.
How many ways can we arrange the word WORD? 4!=24
RULE 2 nPr Read as “Permutation of n objects taken r at a time”. In this rule, not all objects are to be arranged. We just have to choose r objects from n objects. REPETITION IS NOT ALLOWED HERE.
How many 4-digit numbers can be formed from 8 numbers? 8P4 = 1,680
RULE 3 In this rule, in the denominator are the objects that are identical.
How many ways can we arrange the word POOL? 4!/1!x2!x1! = 12
RULE 4 Circular permutation is the total number of ways in which n distinct objects can be arranged around a fix circle
The number of ways of rearranging n distinct objects in a circle is (n-1)!
How many ways can we rearrange 8 people on a round table with no restrictions? (8-1)! = 5,040
RULE 5 The number of permutations of n objects taken r at a time of REPETITION is allowed is n × n × n × n × n × ... × n = n
How many 4-digit number can you make from 10 numbers? 10^4 = 10,000
How many 10 different members of a committee can be formed from 25 people? 25C10 or 25!/(25-10)!10! =3,268,760
Person A has 20 phones, and he gives 12 to person B, how many phones does he have now? 20C12 or 20!/(20-12)!12! = 125,970
In how many ways can a coach of a varsity team pick 15 students from 30 students who are applying? 30C15 or 30!/(30-15)!15! = 155,177,520
In how many ways you can choose 8 of 32 playing cards not considering their order? 32C8 or 32!/(32-8)! = 10,518,300 The playing cards can be chosen in 10 518 300 ways.
