Permutation and Combination Help

Permutation and Combination Help

Permutation is the process of rearranging the given number of elements or objects. Permutation avoids the repletion. Combination is a selection of things or objects or any other from a collection. In combination order of objects is irrelevant.

Permutation formula: P(n,r) = `(n!) / ((n-r)!)`

Combination formula: C(n,r) = `(n!) / (r!(n-r)!)` ,

where, n gives number of things, and r gives number of times.

Between, if you have problem on these topics Boolean Operator, please browse expert math related websites for more help on equivalence relation.

Permutation and Combination Help – Solving Example Problems

See these example problems, it will help you to understand about how to find permutations and combinations.

Example 1: In how many ways can 4 pens be arranged from among 12 pens?

Solution:

This problem involves 12 pens, chosen 4 at a time.

Permutation formula: P(n,r) = `(n!) / ((n-r)!)`

Here, n = 12, r = 4

P(12,4) = `(12!)/((12 - 4)!)` = `(12xx11xx10xx9xx8!) / (8!)` = 11880

There are 11880 possible ways to arrange 5 pens from among 12 pens.

Example 2: In a jar there are 12 balls. In how many ways can 4 balls be chosen from a jar?

Solution:

This problem involves 12 balls, chosen 4 at a time.

Combination formula: C(n,r) = `(n!) / (r!(n-r)!)` ,

Here n = 12, r = 4

C(12,4) = `(12!) / (4!(12 - 4)!)` = `(12xx11xx10xx9) / (4xx3xx2xx1)` = 495

Therefore in 495 different ways can 4 balls be chosen from 12 balls.

Example 3: Calculate the number of permutations and combinations; n = 11, r = 5.

Solution:

Permutation: P(n,r) = `(n!) / ((n-r)!)`

Combination: C(n,r) = `(n!) / (r!(n-r)!)`

Here, n = 11, r = 5.

P(11,5) = `(11!) / ((11 - 5)!)` = `(11xx10xx9xx8xx7xx6!) / (6!)` = 55440

C(11,5) = `(11!) / (5!(11 - 5)!)` = `(11xx10xx9xx8xx7) / (5xx4xx3xx2xx1)` = 462

Therefore permutations = 55440, combination = 462.

Permutation and Combination Help – Solving Practice Problems
Solve these following practice problems, it will help you to get practice on how to find the permutation and combination.

Problem 1: In how many ways can 2 books be arranged from among 10 books?

Problem 2:  In a jar there are 15 orange balls. In how many ways can 6 balls be chosen from a jar?

Problem 3: Calculate the number of permutations and combinations; n = 9, r = 4.

Answer: 1) 90 2) 5005 3) P = 3024, C = 126