Permutation and Combination Online Study

Introduction for permutation and combination online study:
Permutation:

It is the rescheduling of symbols into clear series. When we set things in order, we say we have made an array. When we alter the order, we declare we have changed the arrangement.

Combination:

It is a non sequence collection of unique sizes. In a permutation the order of occurrence of the objects or the arrangement is essential but in combination the order of occurrence of the objects is not important.

Online:

In general, "online" indicates a state of connectivity, In common usage, "online" often refers to the Internet or the World Wide.For the study of these topic , the following example will be more useful

Web.(Source: wiki)

Formulas for study of  permutation and combinations:

Permutation = nPr =` (n!) / ((n - r)!)`

Combination = nCr =` (_nP_r) /(r!) (or) (n!)/(r!(n-r)!)`

Permutation and Combination Online Study - Examples:

Solve online permutation and combination – Example 1:

What is the number of permutations and combinations: n=5; r=3.

Solution:

Formula for permutation:

Permutation = nPr = `(n!) /((n - r)!)`

Step 1: Find the factorial of 5.

5! = 5 × 4 × 3 × 2 × 1 = 120

Step 2: Find the factorial of 5 - 3.

(n - r)! = (5-3)! = 2! =2

Step 3: Divide 120  by 2

Permutation = `120/2` = 60

Combination = nCr = `(_nP_r) /(r!)`

Step 4: Find the factorial of 3.

3! = 3×2×1 = 6

Step 5: Divide 60  by 6.

Combination =` 60/6 ` = 10

The before example will assist you to get the Permutation and Combination manually.

Solve online permutation and combination – Example 2:

What is the number of permutations and combinations: n=8; r =3.

Solution:

Formula for permutation:

Permutation = nPr = `(n!) /((n - r)!)`

Step 1: Find the factorial of 8.

8! = 8 × 7 × 6 × 5×4×3×2×1 = 40 320

Step 2: Find the factorial of 8-3.

(n - r)! = (8-3)! = 5! = 120

Step 3: Divide 40 320 by 120.

Permutation = `40320/120` = 336

Combination = nCr = `(_nP_r) /(r!)`

Step 4: Find the factorial of 3.

3! = 3×2×1 = 6

Step 5: Divide 336 by 6.

Combination = `336/6` = 56

The before example will assist you to get the Permutation and Combination manually.

Solve online permutation and combination – Example 3:

What is the number of permutations and combinations: n= 15; r =2.

Solution:

Formula for permutation:

Permutation = nPr = `(n!) /((n - r)!)`

Step 1: Find the factorial of 15.

15! = 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5×4×3×2×1 = 1 307 674 368 000

Step 2: Find the factorial of 15-2.

(n - r)! = (15-2)! = 13! = 6 227 020 800

Stuck on any of these topics what are prime numbers in math, solve using the substitution method try out some best online tutoring math website.

Step 3: Divide 1 307 674 368 000 by 6 227 020 800.

Permutation = `(1 307 674 368 000)/( 6 227 020 800)`

=  210

Combination = nCr = `(_nP_r) /(r!)`

Step 4: Find the factorial of 2.

2! = 2×1 = 2

Step 5: Divide 210 by 2.

Combination = `210/2 ` = 105

The before example will assist you to get the Permutation and Combination manually.

Permutation and Combination Online Study - Practice Problems:

Practice Problem 1:

What is the number of permutations and combinations: n= 10; r =5.

Answer:

Permutation =30240

Combination = 252

Practice Problem 2:

What is the number of permutations and combinations: n= 50; r =3.

Answer:

Permutation = 117600

Combination = 19600