Online Help for Learning Permutation

In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging in an ordered fashion) objects or values.

Online:

In general, "online" indicates a state of connectivity, In common usage, "online" often refers to the Internet or the World Wide Web.

(Source: wikipedia)
Formula for permutation

Formula:  nPk = (n!)/(n-k!) = n(n-1)(n-2)…..(n-k+1)

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Online help for learning permutation - Examples:

Online help for learning permutation- Example 1:

How much ways can 5 people assemble in 8 sitting rooms in a row?

Solution:

Step 1:

See, we will be using P (8, 5).

Step 2:

(8!)/((8-5)!) = (8*7*6*5*4*3*2*1)/(3*2*1)

Step 3:

(8*7*6*5*4*3*2*1)/(3*2*1) = 40320/6 = 6720.

Step 4:

The answer is 6720.

Online help for learning permutation - Example 2:

Expand 23P5 by canceling factorials:

Solution:

If you want to expand algebraic expressions, you must do so subtracting one from each term.

n! = n (n-1) (n-2)….1

(n-2)! = (n-2) (n-3) (n-4) . . . 1

23P5 = (23!) /((23-5)!) = (23!) /(18!) = 4 037 880

Online help for learning permutation - Example 3:

How many ways can 7 people sitting in 25 session rooms in a row?

Solution:

Step 1:

See, we will be using P (25, 7).

Step 2:

(25!) /((25-7)!)  = (25!)/(18!)

Step 3:

The answer is 2 422 728 000

Online help for learning permutation - Example 4:

Expand 35P5 by canceling factorials:

Solution:

If you want to expand algebraic expressions, you must do so subtracting one from each term.

n! = n (n-1) (n-2)….1

(n-2)! = (n-2) (n-3) (n-4) . . . 1

35P5 = (35!) / ((35-5)!) = (35!) /(30!) = 38 955 840

Online help for learning permutation - Example 5:

Expand 50P10 by canceling factorials:

Solution:

If you want to expand algebraic expressions, you must do so subtracting one from each term.

n! = n (n-1) (n-2)….1

(n-2)! = (n-2) (n-3) (n-4) . . . 1

50P10 = (50!) / ((50-10)!) = (50!) /(40!) = 3.7276043 × 1016

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Online help for learning permutation – Practice Problems:

Online help for learning permutation – Practice Problem 1:

From an assembly of 7 boys and 5 girls, how many different boards consisting of 4 boys and 2 girls can be formed if Rose and Jack refuse to be on the board together?

Find out the permutation or combination problem.

Answer:

270