Suppose you have a checkers board. (8 squares wide and 8 squares long) and you have...
Suppose you have a checkers board. (8 squares wide and 8 squares long) and you
have 16 checkers.
-
How many ways can the checkers be placed on the board if there are no restrictions?(3)
-
Now, suppose you must place 2 checkers in each row. How many ways can this be accomplished?(2)
Homework Answers
1st part :
select 16 squares from 64 to place on the board
no. of ways = 64C16
= 64!/(16! * (64-16)!)
= 4.8852694*10^14
in 4.8852694*10^14 ways the checkers can be placed on the board if there are no restrictions
2nd part :
select 2 squares out of 8 squares in each of the 8 rows
no. of ways = 8C2*8C2*8C2*8C2*8C2*8C2*8C2*8C2
= (8C2)^8
= 28^8
= 377801998336
no. of ways if you must place 2 checkers in each row = 377801998336
(please UPVOTE)
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