Math / Discrete

QuestionA college offers 2 introductory courses in history, 4 in science, 2 in mathematics, 4 in philosophy, and 1 in English. a. If a student takes one course in each area during her first semester, how many course selections are possible? $\square$ b. If a part-time student can afford to take only one introductory course, how many selections are possible? $\square$

Studdy Solution

STEP 1

1. Each course in a different subject area is independent of the others.
2. The student can choose only one course per subject area for part (a).
3. For part (b), the student can choose only one course from all available introductory courses.

STEP 2

1. Calculate the number of course selections possible when taking one course in each area.
2. Calculate the number of selections possible when taking only one course overall.

STEP 3

Identify the number of courses available in each subject area: - History: 2 courses - Science: 4 courses - Mathematics: 2 courses - Philosophy: 4 courses - English: 1 course

STEP 4

For part (a), multiply the number of courses available in each subject area to find the total number of course selections possible:
$2 \times 4 \times 2 \times 4 \times 1$

STEP 5

Calculate the product:
$2 \times 4 = 8$ $8 \times 2 = 16$ $16 \times 4 = 64$ $64 \times 1 = 64$

STEP 6

For part (b), calculate the total number of introductory courses available by summing the courses in each subject area:
$2 + 4 + 2 + 4 + 1$

STEP 7

Calculate the sum:
$2 + 4 = 6$ $6 + 2 = 8$ $8 + 4 = 12$ $12 + 1 = 13$
The number of course selections possible for part (a) is:
$\boxed{64}$
The number of selections possible for part (b) is:
$\boxed{13}$

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Studdy Solution

STEP 1

1. Each course in a different subject area is independent of the others.
2. The student can choose only one course per subject area for part (a).
3. For part (b), the student can choose only one course from all available introductory courses.

STEP 2

1. Calculate the number of course selections possible when taking one course in each area.
2. Calculate the number of selections possible when taking only one course overall.

STEP 3

Identify the number of courses available in each subject area: - History: 2 courses - Science: 4 courses - Mathematics: 2 courses - Philosophy: 4 courses - English: 1 course

STEP 4

For part (a), multiply the number of courses available in each subject area to find the total number of course selections possible:
$2 \times 4 \times 2 \times 4 \times 1$

STEP 5

Calculate the product:
$2 \times 4 = 8$ $8 \times 2 = 16$ $16 \times 4 = 64$ $64 \times 1 = 64$

STEP 6

For part (b), calculate the total number of introductory courses available by summing the courses in each subject area:
$2 + 4 + 2 + 4 + 1$

STEP 7

Calculate the sum:
$2 + 4 = 6$ $6 + 2 = 8$ $8 + 4 = 12$ $12 + 1 = 13$
The number of course selections possible for part (a) is:
$\boxed{64}$
The number of selections possible for part (b) is:
$\boxed{13}$

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Studdy Solution

STEP 1

1. Each course in a different subject area is independent of the others.2. The student can choose only one course per subject area for part (a).3. For part (b), the student can choose only one course from all available introductory courses.

STEP 2

1. Calculate the number of course selections possible when taking one course in each area.2. Calculate the number of selections possible when taking only one course overall.

STEP 3

Identify the number of courses available in each subject area: - History: 2 courses - Science: 4 courses - Mathematics: 2 courses - Philosophy: 4 courses - English: 1 course

STEP 4

For part (a), multiply the number of courses available in each subject area to find the total number of course selections possible:2×4×2×4×1 2 \times 4 \times 2 \times 4 \times 1 2×4×2×4×1

STEP 5

Calculate the product:2×4=8 2 \times 4 = 8 2×4=8 8×2=16 8 \times 2 = 16 8×2=16 16×4=64 16 \times 4 = 64 16×4=64 64×1=64 64 \times 1 = 64 64×1=64

STEP 6

For part (b), calculate the total number of introductory courses available by summing the courses in each subject area:2+4+2+4+1 2 + 4 + 2 + 4 + 1 2+4+2+4+1

STEP 7

Calculate the sum:2+4=6 2 + 4 = 6 2+4=6 6+2=8 6 + 2 = 8 6+2=8 8+4=12 8 + 4 = 12 8+4=12 12+1=13 12 + 1 = 13 12+1=13 The number of course selections possible for part (a) is:64 \boxed{64} 64​The number of selections possible for part (b) is:13 \boxed{13} 13​

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1. Each course in a different subject area is independent of the others.
2. The student can choose only one course per subject area for part (a).
3. For part (b), the student can choose only one course from all available introductory courses.

1. Calculate the number of course selections possible when taking one course in each area.
2. Calculate the number of selections possible when taking only one course overall.

For part (a), multiply the number of courses available in each subject area to find the total number of course selections possible:
$2 \times 4 \times 2 \times 4 \times 1$

Calculate the product:
$2 \times 4 = 8$ $8 \times 2 = 16$ $16 \times 4 = 64$ $64 \times 1 = 64$

For part (b), calculate the total number of introductory courses available by summing the courses in each subject area:
$2 + 4 + 2 + 4 + 1$

Calculate the sum:
$2 + 4 = 6$ $6 + 2 = 8$ $8 + 4 = 12$ $12 + 1 = 13$
The number of course selections possible for part (a) is:
$\boxed{64}$
The number of selections possible for part (b) is:
$\boxed{13}$