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.
To determine the number of different examinations, we need to consider the possible blood types for each blood sample.
Given that there are 8 standard classifications of blood type, the first blood sample can have any of these 8 types.
For the second blood sample, since it cannot have the same type as the first blood sample, there are 7 remaining types to choose from.
Similarly, for the third blood sample, there are 6 remaining types to choose from, as it cannot have the same type as the first and second samples.
To find the total number of different examinations, we multiply the number of choices for each blood sample:
Total number of examinations = Number of choices for 1st sample * Number of choices for 2nd sample * Number of choices for 3rd sample
Total number of examinations = 8 * 7 * 6
Calculating the above expression:
Total number of examinations = 336
Therefore, there are 336 different examinations that can be given where no two of the blood samples have the same type.
To find the number of different examinations that can be given, we need to consider the number of choices for each blood sample and multiply them together.
Given that there are 8 standard classifications of blood type, the first blood sample can have any 1 of the 8 blood types. The second blood sample can have any 1 of the remaining 7 blood types (since it cannot be the same as the first sample). Similarly, the third blood sample can have any 1 of the remaining 6 blood types.
Therefore, the total number of different examinations is calculated as:
8 * 7 * 6 = 336
Hence, there can be 336 different examinations, where no two of the samples provided to the candidate have the same type.
8 choose 3
=8C3
=8!/((8-3)!3!)
=8*7*6/(1*2*3)
=56