Question

Padma has room to line up 8 figurines in a display case.

How many different ways can she arrange the figurines in the display case?

Enter your answer in the box.

ways

Answer 1

• Total figurines=8

Total ways for n object is n!

Total ways

• 8!
• 8×7×6×5×4×3×2×1
• 40320ways

Answer 2

40320

Explanation:

Imagine placing the figurines on the shelf one at a time.

You have:

• 8 choices for the first figurine
• 7 choices for the second figurine
• 6 choices for the third figurine
• 5 choices for the fourth figurine
• 4 choices for the fifth figurine
• 3 choices for the sixth figurine
• 2 choices for the seventh figurine
• and 1 choice for the last (eighth) figurine

So there are 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 8! = 40320 different ways she can arrange the figurines.