Problems with math…?
1. Wayne has 6 autographed baseballs and room for 4 in his display case. How many arrangements can he make.
2. ten business cards have been placed in a bowl at a restaurant. 4 names are drawn to win a free lunch. How many different ways can the four names be drawn.
3. How many ways can 8 people line up for a picture?
Thank you for your help. Please if you can, explain how you got your answers.
PROBLEM 1:
Do you care about the order of the items in the display case? I’ll assume so. Then you have 6 choices for the first position, 5 choices for the second position, 4 choices for the third position and 3 choices for the fourth position.
6 x 5 x 4 x 3 = 360 ways.
P.S. If you *don’t* care about order, then divide by the ways to arrange 4 items (4!) –> 360/24 = 15 ways
PROBLEM 2:
We assume the order of drawing doesn’t matter, just the people that are on the list to get a free lunch.
This is 10C4 –> (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)
= 210 ways
PROBLEM 3:
8 for the 1st position, 7 for the 2nd, etc.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 40,320 ways
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