Question

Find the probability of each event. A gambler places a bet on a horse race. To win, he must pick the top three finishers in any order. Eight horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win his bet?

Answer 1

Answer: $\dfrac{1}{56}$

Step-by-step explanation:

Total horses = 6

Number of ways to choose top 3 finishers in order = 3! = 6

Number ways to select 3 horses out of 8 in order = $^8P_3$  [By permutations]

$=\dfrac{8!}{(8-3)!}=\dfrac{8!}{5!}=8\times7\times6=336$

Now, the probability that the gambler will win his bet =

$\dfrac{\text{Number of ways to choose top 3 finishers }}{\text{Number ways to select 3 horses out of 8 in order}}$

$=\dfrac{6}{336}\\\\=\dfrac{1}{56}$

Hence, the required probability =  $\dfrac{1}{56}$