In how many different orders can you line up 8 cards on a table.

Solution:

Given, there are 8 cards on a table.

We have to find the number of different orders we can line up 8 cards on a table.

Permutations of n different objects taken r at a time is, the total number of ways in which n objects can be arranged at r places in a line and is given by

ⁿPr = n! / (n - r)!

Total number of cards, n = 8

So, ⁶P₆ = 8! / (8 - 8)!

= 8! / (0!)

We know, 0! = 1

So, ⁶P₆ = 8!

= 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 56 × 30 × 24

= 56 × 720

= 40320 ways

Therefore, we can line up cards in 40320 ways.

In how many different orders can you line up 8 cards on a table.

Summary:

In 40320 different orders we can line up 8 cards on a table.