Question

Pat, Jo, Al, and Dan are finalists in a talent contest. How many different ways can Pat, Jo, Al, and Dan finish in first, second, third, and fourth place in the contest?

23 ways
10 ways
24 ways
12 ways

Answer 1

Answer:

24 ways!

Step-by-step

Pat, Jo, Al, Dan

Pat, Al, Dan, Jo

Pat, Dan, Jo, Al

Pat, Jo, Dan, Al

Pat, Al, Jo, Dan

Pat, Dan, Al, Jo List all permutations beginning with Pat.

Jo, Al, Dan, Pat

Jo, Dan, Pat, Al

Jo, Pat, Al, Dan

Jo, Al, Pat, Dan

Jo, Dan, Al, Pat

Jo, Pat, Dan, Al List all permutations beginning with Jo.

Al, Dan, Pat, Jo

Al, Pat, Jo, Dan

Al, Jo, Dan, Pat

Al, Pat, Dan, Jo

Al, Dan Jo, Pat

Al, Jo, Pat, Dan List all permutations beginning with Al.

Dan, Pat, Jo, Al

Dan, Jo, Al, Pat

Dan, Al, Pat, Jo

Dan, Jo, Pat, Al

Dan, Pat, Al, Jo

Dan, Al, Jo, Pat List all permutation beginning with Dan.

There are 24 ways for Pat, Jo, Al, and Dan to finish in first, second, third, and fourth place in the contest.

Answer 2

Using permutations, they are 24 different ways Pat, Jo, Al and Dan finish  in first, second, third, and fourth place in the contest.  

What is permutations?

A permutations is "a mathematical calculations of the number of ways  a particular data can be arranged".

According to the question,

Pat, Jo, Al and Dan finish  in first, second, third, and fourth place in the contest.

Formula for Permutation $nP$ₓ = $\frac{n!}{(n-x)!}$  where 'n' number of items set and 'x' is the item taken for Permutation.

In order to find number of ways first, second, third, and fourth place are arrangement or Permutation in the contest.

First, second, third and fourth are four places can be obtained by Pat, Jo, Al and Dan by four position

Formula for permutation P(n , n) = n!. Using this formula P(4,4) = 4!

= 1×2×3×4  =24 ways.

Hence, using permutations, they are 24 different ways Pat, Jo, Al and Dan finish  in first, second, third, and fourth place in the contest.  

Learn more about Permutation here

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