**Please show all steps & explain the reasoning behind the solution to this prob

Question

**Please show all steps & explain the reasoning behind the solution to this problem.
**Please ignore my writing & answer both parts a & b. Tks.
Best Regards,
JF

3. (16 points) (8 points) Three awards (research, teaching and service) will be given to a class of 18 graduate students in a statistics department. If each student can receive at most one award, how many possible selections are a. (18-357-1 51 -3 15 b. (8 points) Find the probability of getting a sum of 7 or a difference of 4 when a pair of fair dice is tossed.

Explanation / Answer

Answer to the question is as follows:

3a. The number of ways this can be done is :

18P3 = 18!/15! = 4896

3b.

Sum of 7 can be had in : (6,1),(1,6),(2,4),(4,2),(3,3) : 5 ways
Difference of 4 can be had in (6,2),(2,6),(1,5),(5,1) : 4 ways
So, 9 ways out 6*6 =36 possible ways.
Hence, the answer is 9/36 = 1/4 or .25 is the probability of getting sum of 7 or a difference of 4

Answer: 1/4 of .25

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