hi guys its gurbaz

The definition of n!, pronounced n factorial is (n)(n - 1)(n - 2). . . (3)(2)(1)

For example:
3! = (3)(2)(1) = 6
4! = (4)(3)(2)(1) = 24
5! = (5)(4)(3)(2)(1) = 120
6! = (6)(5)(4)(3)(2)(1) = 720

The number of permutations of n objects taken r at a time is:

Example 1:

Find the number of ways to arrange 4 people in groups of 3 at a time where order matters.

Solution:

There are 24 ways to arrange 4 items taken 3 at a time when order matters.

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Example 2:

Find the number of ways to arrange 6 items in groups of 4 at a time where order matters.

Solution:

There are 360 ways to arrange 6 items taken 4 at a time when order matters.

The number of combinations of a group of n objects taken r at a time is:

Example 3:

Find the number of ways to take 4 people and place them in groups of 3 at a time where order does not matter.

Solution:

Since order does not matter, use the combination formula.

There are 4 ways to arrange 4 items taken 3 at a time when order does not matter.

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Example 4:

Find the number of ways to take 20 objects and arrange them in groups of 5 at a time where order does not matter.

Solution:

There are 15,504 ways to arrange 20 objects taken 5 at a time when order does not matter.

_______________________________Example 7:

Determine the total number of five-card hands that can be drawn from a deck of 52 cards.

Solution:
When a hand of cards is dealt, the order of the cards does not matter. If you are dealt two kings, it does not matter if the two kings came with the first two cards or the last two cards. Thus cards are combinations.


There are 52 cards in a deck and we want to know how many different ways we can put them in groups of five at a time when order does not matter. The combination formula is used.

C(52,5) = 2,598,960

Therefore there are 2,598,960 different ways to create a five-card hand from a deck of 52 cards.