Question

Contestants A, B, C, D, and E are in a 10K race. How many different ways can a race with 5 runners be completed? (Assume there is no tie.)

In how many ways can B finish first and D finish second?

What is the probability that B finishes first and D finishes second? Enter a reduced fraction or decimal.

Answer 1

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:

$\mathbf{_nP_r = \dfrac{n!}{(n-r)!}}$

The number of different ways in which a race with 5 runners can be completed can be estimated by using permutation.

$\mathbf{_nP_r = \dfrac{5!}{(5-5)!}}$

$\mathbf{= \dfrac{5!}{1!}}$

= 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:

$= \mathbf{3P_3 = 3!}$

= 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:

$\mathbf{P( B \ and \ D) = \dfrac{2!}{5!}}$

$\mathbf{P( B \ and \ D) =0.01667}$

Learn more about permutation here:

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