A car race qualifier has 10 participants. How many different ways can the top 6 cars cross the finish line?
1 answer:
Answer:
There are 151,200 different ways.
Step-by-step explanation:
For solving this question, we need the concept of permutation, the permutation gives as the number of ordered arrangement that can be made chosen k elements from a group of n elements. it is calculated as:
So, in this case, we need to find the number of ways in which 6 top participants from the 10 participants can cross the finish line.
Now, we can replace n by 10 and k by 6 and calculate the number of permutations as:
Finally, there are 151,200 different ways in which the top 6 cars can cross the finish line.
You might be interested in
Answer:
The probability function of X and Y is
With k in {1,2,3,4,5,6}
Step-by-step explanation:
We can naturally assume that X and Y are independent. Because of that, P(X=a, Y=b) = P(X=a) * P(Y=b) for any a, b.
Note that, since the die is honest, then P(X=k) = 1/6 for any k in {1,2,3,4,5,6}. We can conclude as a consequence that P(X=k, Y=l) = P(Y=l)/6 for any k in {1,2,3,4,5,6}.
Y has a binomial distribution, with parameters n = 3, p = 1/2. Y has range {0,1,2,3}. Lets compute the probability mass function of Y:
Thus, we can conclude that the joint probability function is given by the following formula
For any k in {0,1,2,3,4,5,6}