The Department of Mathematics and Statistics is currently su

The Department of Mathematics and Statistics is currently submitting a list of scholarship candidates to the Department Head, the best four are to receive the Ernest Enns Scholarship in Mathematical Science. The submitted list has been finalized and consists of 15 students: 4 in Statistics, 4 in AMAT, 5 in PMAT, and 2 in Acturial Science. Assuming the sample space is equivariant, What is the probability that \"Non-Math\" (meaning students in STAT or ACSC) students will receive all four scholarships? What is the probability that the four scholarships will be filled by one Statistics student, two AMAT students, and one ACSC student?

Solution

A)

There are 15C4 = 1365 ways to choose 4 students.

There are 9C4 = 126 ways to choose 4 non-math students.

Thus,

P(all non math) = 126/1365 = 0.092307692 [answer]

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b)

There are (4C1)(4C2)(2C1) = 48 ways to do that task.

Thus,

Probability = 48/1365 = 0.035164835 [answer]