Answer:
a) 45 possible outcomes
b) 55 possible outcomes
Step-by-step explanation:
Given:
- Total cavities = 12
- Selection = 3 parts
- Non-conforming cavities = 2
Find:
a) How many samples contain exactly 1 nonconforming part?
b) How many samples contain at least 1 nonconforming part?
Solution:
- The question asks for the use of combinations to express the outcomes for each scenario.
- For first part, we want the inspector to pick exactly one non-conforming part among 3 selected. So let us say that he has already chosen that one non conforming cavity. Now he has to make 2 more selections out of total conforming cavities = 12 - 2 = 10 conforming cavities. Hence, the total possible outcome is to chose 2 randomly from 10 conforming cavities.
( Exactly 1 ) 10C2 = 45 possible outcomes
- The second part entails that at-least 1 non-conforming cavity is selected. To choose exactly 1 non conforming we calculated above. In the similar way calculate for selecting exactly 2 non-conforming cavities. The total possible outcome would be to choose from 10 conforming and we choose 1 from it:
( Exactly 2 ) 10C1 = 10 possible outcomes
- Hence, for at-least 1 non conforming cavity being selected we same the above two cases calculated:
(At-least 1 ) = ( Exactly 1 ) + ( Exactly 2 )
(At-least 1 ) = 45 + 10 = 55 possible outcomes
Team A) 45 people
Team B) 55 people
A)There are two ways to solve this problem, finding the number of combinations possible for Team B, or the number of combinations possible for Team A.
Team A
It's a given that 20 mathematicians are on team A, which leavs the other 25 people for team A to be chosen from a pool of 80 (100- 20 mathletes)
80-C-25 = 80! / (25!/(80-25)!) =<span>363,413,731,121,503,794,368
</span>or 3.63 x 10^20
Solving using Team B
Same concept, but choosing 55 from a pool of 80 (mathletes excluded)
80-C-25 = 80! / (55!(80-55!) = 363,413,731,121,503,794,368
or 3.63 x 10^20
As you can, we get the same answer for both.
B)
If none of the mathematicians are on team A, then we exclude the 20 and choose 45:
80-C-45 = 80! / (45!(80-45)!) = <span>5,790,061,984,745,3606,481,440
or 5.79 x 10^22
Note that, if you solve from the perspective of Team B (80-C-35), you get the same answer</span>
Answer:
I beleive A is quadratic, but im not sure
Step-by-step explanation:
Answer: valu of a
Step-by-step explanation: I Did the test
