Question

If the order of objects is of​ importance, how many ways can eight objects be selected three at a​ time?

There are ____ different ways to pick three objects at a time.

If the order of objects is not of​ importance, how many ways can nine objects be selected three at a​ time? Why is this result different from the result when order​ matters?

There are ____ different ways to select three objects at a time.

Answer 1

When order matters,

From the 8 objects 3 could be selected at a time by ⁸P₃ ways.

In general, ⁿP_r = n! / (n-r)!

So,

⁸P₃ = 8! / (8-3)!

= 8! / 5!

= 336

There are 336 different ways to pick three objects at a time

When order is not important,

From the 9 objects 3 could be selected at a time by ⁹C₃ ways.

In general,

ⁿC_r = n! / [ (n-r)! * r! ]

Therefore

⁹C₃ = 9! / [ (9-3)! * 3! ]

= 84

There are 84 different ways to select three objects at a time.

When order matters, selecting an objects has a particular order.

Rather in combination, when order does not matter selecting an objects randomly from all

available objects.