The race with 5 runners can be completed in 120 ways. The number of ways in which B finish first and D finish second is 6 ways. The probability that B finishes first and D finishes second is 0.01667
A permutation is referred to as the number of ways in which linear elements can be arranged in an orderly manner. It is usually expressed by the formula:
[tex]\mathbf{_nP_r = \dfrac{n!}{(n-r)!}}[/tex]
The number of different ways in which a race with 5 runners can be completed can be estimated by using permutation.
[tex]\mathbf{_nP_r = \dfrac{5!}{(5-5)!}}[/tex]
[tex]\mathbf{= \dfrac{5!}{1!}}[/tex]
= 120 ways
If we fix B at first and D at second, then, the number of ways in which B and D can finish first and second respectively is:
[tex]= \mathbf{3P_3 = 3!}[/tex]
= 6 ways
We know that the total number of ways A, B, C, D, and E can finish the race = 5!
The total number of ways B and D finish first and second is = 2!
∴
The probability that B and D finish 1st and 2nd respectively can be computed as:
[tex]\mathbf{P( B \ and \ D) = \dfrac{2!}{5!}}[/tex]
[tex]\mathbf{P( B \ and \ D) =0.01667}[/tex]
Learn more about permutation here:
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