Question

Q10.       A student wishes to take

an English Course (offered at 8, 10, 11 and 12),

a Math Course (offered at 9, 10, 12 and 1) and

a Comp Sci Course (offered at 9, 11, 12 and 1)

                How many different schedules are possible so that they make take all three courses?

Answer 1

There are four timings each available for the three different courses.

Let us first try to list down all possibilities.

The listing will be in the order English, Math, Comp Sci.

8, 9, 11

8, 9, 12

8, 9, 1

8, 10, 9

8, 10, 11

8, 10, 12

8, 10, 1

8, 12, 9

8, 12, 11

8, 12, 1

8, 1, 9

8, 1, 11

8, 1, 12

The number of combinations for an English course starting at 8 is 13.

10, 9, 11

10, 9, 12

10, 9, 1

10, 12, 9

10, 12, 11

10, 12, 1

10, 1, 9

10, 1, 11

10, 1, 12

The number of combinations for an English course starting at 10 is 9.

11, 9, 12

11, 9, 1

11, 10, 9

11, 10, 12

11, 10, 1

11, 12, 9

11, 12, 1

11, 1, 9

11, 1, 12

The number of combinations for an English course starting at 11 is 9.

12, 9, 11

12, 9, 1

12, 10, 9

12, 10, 11

12, 10, 1

12, 1, 9

12, 1, 11

The number of combinations for an English course starting at 12 is 7.

Thus, the total number of different schedules possible is 13+9+9+7= 38.