Permutations in Math

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. Informally, a permutation of a set of values is an arrangement of those values into a particular order. Thus there are six permutations of the set {1,2,3}, namely [1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2], and [3,2,1]. (Source – Wikipedia.)

Example problems for permutations in math:

Example 1

1) How many permutations of 5 apparatus are probable from 2 apparatus. what is a permutation in given math problem?

Solution:

By means of the formula we can evaluate the answer,

P (n, r) = n! / (n – r)!

Here, n = 5, r = 2

P (5, 2) = 5! / (5–2)!

P (5, 2) = 5! / 3!

=   `(5xx4xx3xx2xx1)/ (3xx2xx1)`

Now 3, 2, 1 gets crossed out

= 5 x 4

= 20

Answer is: 20

Example 2

How many permutations of 9 files are possible from 5 books. what is a permutation in given math problem?

Solution:

Formula for calculate permutations,

P (n, r) =n! / (n – r)!

Now, n = 9

r = 5

P (9, 5) = 9! / (9 – 5)!

P (9, 5) = 9! / 4!

= `(9 *8 * 7 * 6 *5 * 4 *3 *2 *1)/ (5 * 4 *3 *2 *1)`

Here 5, 4, 3, 2, 1 gets crossed out

= 9x 8 x 7x 6

= 3,024

The answer is: 3, 024

Example 3

How many ways can 6 graduates from group of 15 are lined up for a function. what is a permutation in given math problem?

Solution:

There are 15P6 possible permutations from a group of 15.

15P6 = (15!)/(15-6!)

= (15!)/ (9!)

= 15x 14x 13x 12x 11x 10

= 3, 603, 600 different lineups.

The answer is: 3, 603, 600 different lineups.

Example 4

How many ways can 3 kids from group of 13 are lined up for a photograph. what is a permutation in given math problem?

Solution:

There are 13P3 possible permutations of 3 students from a group of 13.

13P3 = (13!)/ (13- 3!)

= (13!)/ (10!)

= 13 x 12 x 11

= 1716 different lineups.

The answer is: 1716 different lineups.

My forthcoming post is on Divide Fractions by Whole Numbers and cbse sample papers for class 9 science will give you more understanding about Algebra.

Practice problems for what is a permutations in math:

Practice problem -1

1) How many permutations of 9 components are possible from 2 elements. what is a permutation in given math problem?

Ans: 72

Practice problem -2

2) How many ways can 3 girls from group of 14 are lined up for a photograph?

Ans: 2184

Practice problem -3

3) How many permutations of 17 books are possible from 4 books?

Ans: 57, 120

Practice problem -4

4) How many 4-digit numbers can be ordered from the digits 1, 2, 3, 4, and 5, if each digit is unique. what is a permutation in given math problem?

Ans: 120.