Question

A student entering a doctoral program in educational psychology is required to select three courses from the list of courses provided as part of his or herprogram(a) List all possible three-course selections.(6) Comment on the likelihood that EPR 669, EPR 634, and EPR 679 will be selectedClick the icon to view the course list(a) Select all the possible three-course selections below.A. 669,644, 679C. 669,634, 644DE 669.669, 634G. 669, 679, 6561669,634, 656K. 669, 669M. 634, 644,679(b) There is a chance that these courses will be selected.(Simplify your answer)B. 634, 644, 656D. 669. 644, 656OF 634, 679,656DH. 669,634, 679J. 656, 612, 656OL. 644,679, 656N. 644, 656, 644

Answer 1

(a) We need to find the number of combinations of selecting 3 courses of a group of 5 courses.

The number of combinations of n things chosen r at a time is found using:

`_nC_r=(n!)/(r!(n-r)!)`

Substituting with n = 5 and r = 3, we get:

`_nC_r=(n!)/(r!(n-r)!)=(5!)/(3!(5-3)!)=(5\cdot4\cdot3!)/(3!2!)=(5\cdot4)/(2\cdot1)=10`

The 10 possible combinations are:

• 669, 644, 679

,

• 669, 634, 644

,

• 669, 679, 656

,

• 669, 634, 656

,

• 634, 644, 679

,

• 634, 644, 656

,

• 669, 644, 656

,

• 634, 679, 656

,

• 669, 634, 679

,

• 644, 679, 656

(b) There is a 1 in 10 chance that these courses will be selected