There are 8 standard classifications of blood type. An examination for prospective laboratory technicians consists of having each candidate determine the type for 3 blood samples. How many different examinations can be given of no 2 of the samples provided for the candidate have the same type.
Well, if there are 8 standard classifications of blood type and no two samples can have the same type, then for the first blood sample, the candidate has 8 options. For the second blood sample, since one type has already been chosen, there are 7 options remaining. Finally, for the third blood sample, with two types already chosen, there are 6 options left. To find the total number of different examinations, we multiply these options together: 8 × 7 × 6 = 336 different examinations. So, a prospective laboratory technician has 336 ways to potentially determine the blood types of the 3 samples. Just remember, the patients might get a bit dizzy from all the needle pricks!
To find the number of different examinations that can be given, we can consider the problem in two steps.
Step 1: Determine the different types of blood samples that can be used for the first sample. Since there are 8 standard classifications of blood type, there are 8 options for the first sample.
Step 2: Determine the different types of blood samples that can be used for the second and third samples. Since we don't want any two samples to have the same type, for the second sample, there are only 7 options left. Similarly, for the third sample, there are 6 options remaining.
To find the total number of different examinations, we multiply the number of options for each step:
Number of different examinations = Number of options for the first sample * Number of options for the second sample * Number of options for the third sample
Number of different examinations = 8 * 7 * 6 = 336
Therefore, there can be 336 different examinations where no two samples have the same blood type.
To find the number of different examinations that can be given, we can consider the available blood types and the number of samples.
Since there are 8 standard classifications of blood type, the first candidate can choose any of the 8 blood types for the first sample. Similarly, for the second sample, the candidate can choose from the remaining 7 blood types. Finally, for the third sample, there are 6 blood types left.
To find the total number of different examinations, we multiply the number of choices for each sample. Therefore, the number of different examinations is calculated as:
8 (choices for the first sample) * 7 (choices for the second sample) * 6 (choices for the third sample) = 336 different examinations.
So, 336 different examinations can be given where no two of the provided samples have the same blood type.