In how many different orders can you line up 8 cards on a shelf?

1 Answer
Mar 5, 2018

#40,320# ways

Explanation:

Given: 8 cards on a shelf

In the 1st spot you can have up to 8 different cards.

The 2nd spot can only have 7 since a card is already in the 1st spot.

The 3rd spot can only have 6 since a card is already in the 1st spot and the 2nd spot.

The 4th spot can have 5 different cards

The 5th spot can have 4 different cards

The 6th spot can have 3 different cards

The 7th spot can have 2 different cards

The 8th spot can have 1 card

The number of different arrangements:

#= 8*7*6*5*4*3*2*1 = 8! = 40,320#