# Solve for the unknown in each item, and then answer the questions that follow. 3. p(n, 3) = 60

Answers: 2

## Answers

Solve for the unknown in each item, and then answer the questions that follow. 3. p(n, 3) = 60...

PERMUTATION is one of the many different ways or forms in which something exists or can be arranged. Permutation is a particular ordering of a set of objects, an arrangement of objects, rays or gamma rays. The phenomenon is widely used for elemental analysis and chemical analysis of minerals.

Solution:

The permutation of n objects taken r at a time is:

P(n, r) = n!/ (n-r)! where n ≥ r.

Let n = 5

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

P(5, 3) = 5*4*3*2*1/( 5-3) !

P(5, 3) = 5*4*3*2*1/(2)!

P(5, 3) = 5*4*3*2*1/2*1

P(5, 3) = 120/ 2

P(5, 3) =60

Thus, there are 60 possible ways .

2.30,240

3. 6,720

PERMUTATION is one of the many different ways or forms in which something exists or can be arranged. Permutation is a particular ordering of a set of objects, an arrangement of objects, rays or gamma rays. The phenomenon is widely used for elemental analysis and chemical analysis of minerals.

Solution:

The permutation of n objects taken r at a time is:

P(n, r) = n!/ (n-r)! where n ≥ r.

Given: P(12, r) = 1320

Solution: let r = 3

P(12, 3) = 12!/(12-3)!

P(12, 3) = 12*11*10* 9*8*7 *6*5*4*3*2*1 /9 !

P(12, 3) = 12*11*10* 9*8*7 *6*5*4*3*2*1/ * 9*8*7 *6*5*4*3*2*1

P(12, 3) = 479001600 / 362880

P(12, 3) = 1320

PERMUTATION is one of the many different ways or forms in which something exists or can be arranged. Permutation is a particular ordering of a set of objects, an arrangement of objects, rays or gamma rays. The phenomenon is widely used for elemental analysis and chemical analysis of minerals.

Solution:

The permutation of n objects taken r at a time is:

P(n, r) = n!/ (n-r)! where n ≥ r.

Given: P(13, r) = 156

Solution: let r = 2

P(13, 2) = 13!/(13-2)!

P(13, 2) = 13*12*11*10* 9*8*7 *6*5*4*3*2*1 /11!

P(13, 2) = 13* 12*11*10* 9*8*7 *6*5*4*3*2*1/11*10 * 9*8*7 *6*5*4*3*2*1

P(13, 2) = 6227020800 / 39916800

P(13, 2) = 156

Solution:

The permutation of n objects taken all at time is

P(n, n) = n!

Given: P(6, 6) =

Solution :

Given: P(6, 6) = 6*5*4*3*2*1

P(6, 6) = 30 *4*3*2*1

Given: P(6, 6) = 120*3*2*1

Given: P(6, 6) = 360*2*1

Given: P(6, 6) = 720*1

Given: P(6, 6) = 720

There are 720 numbers to be arranged .

The permutation of n objects taken r at a time is:

P(n, r) = n!/ (n-r)! where n ≥ r.

Given: P(n, 3) = 504

Let n = 9

P(9, 3) = 9!/(9-3)!

P(9, 3) = 9*8*7*6*5*4*3*2*1/( 9-3) !

P(9, 3) = 9*8*7 *6*5*4*3*2*1/(6)!

P(9, 3) = 362880/6*5*4*3*2*1

P(9, 3) = 362880/ 720

P(9, 3) =504

Solution:

The permutation of n objects taken r at a time is:

P(n, r) = n!/ (n-r)! where n ≥ r.

Given: P(n, 4) = 3024

Solution: let n = 9

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

P(9, 4) = 9*8*7 *6*5*4*3*2*1 /( 5) !

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

P(9, 4) = 362880/ 120

P(9, 4) = 3024

Solution:

The permutation of n objects taken r at a time is:

P(n, r) = n!/ (n-r)! where n ≥ r.

Given: P(10, 5) =

Solution:

P(10, 5) = 10!/(10-5)!

P(10, 5) = 10* 9*8*7*6*5*4*3*2*1/( 10-5) !

P(10, 5) = 10*9*8*7 *6*5*4*3*2*1/(5)!

P(10, 5) = 3628800 /5*4*3*2*1

P(10, 5) = 3628800/ 120

P(10, 5) = 30240