In regional spelling bee, the 8 finalists consist of 3 boys and 5 girls. Find the number of sample point the sample space S for
1 answer:
Answer:
i) A total of 40320 different arrangements
ii) For the initial 3 spots, there are 336 different combinations.
Step-by-step explanation:
Given: The total finalists = 8
The count of boys = 3
The count of girls = 5
To determine the number of sample point in the sample space S for possible arrangements, we calculate the factorial of 8!
The number of possible arrangements equals 8!
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
= 40320
ii) Among the 8 finalists, we must select the first 3 spots. The sequence matters, hence we utilize permutation.
nPr =
Here n = 8 and r = 3
Substituting n = 8 and r = 3 into the formula, we arrive at
8P3 =
=
= 6.7.8
= 336
Thus, there are 336 different arrangements for the first 3 spots.
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The question appears to be incomplete. Here’s the complete inquiry:
Samir is quite skilled with the gun. When he targets a specific aim at the shooting range, he has a 0.95 probability of striking it. On one occasion, Samir sets out to shoot 10 targets consecutively.
If he has the same chance of hitting each of the 10 targets, what is the likelihood that he will miss at least one?
Response:
40.13%
Step-by-step breakdown:
Let 'A' represent the event of successfully hitting all targets in 10 trials.
The complement of 'A' is
Now, since Samir has a consistent probability of hitting each target at 0.95.
Now,
We know that the combined probability of an event and its complement equals 1.
<pThus,Consequently, the probability that he misses at least one target among 10 attempts is 40.13%.
Answer:
together they rake leaves in one minute.
Step-by-step explanation:
If Maya takes x minutes to rake, then in one minute, she rakes leaves.
For Carla, if her raking takes y minutes, in one minute she rakes leaves.
Thus, to find the amount they work together in one minute, we add both of their contributions for that minute, resulting in:
Finally, simplifying this expression gives:
As a result, they collectively rake leaves in a minute.