True/False — Permutations, Combinations & Multiplication Rule
Pick
True
or
False
for each student-life scenario. Feedback appears immediately.
1) Outfits: You have 5 shirts, 3 pants, and 2 shoes. “Total outfits =
5×3×2 = 30
.”
True
False
2) Presentations: 10 students, 4 ordered speaking slots. “Number of lineups =
P(10,4) = 10×9×8×7 = 5,040
.”
True
False
3) Project team: Choose 3 teammates from 12 students (order doesn’t matter). “Number of teams =
C(12,3) = 220
.”
True
False
4) Locker codes: 4-digit code using 0–9, digits can repeat. “Number of codes =
P(10,4) = 5,040
.”
True
False
5) Photos: From 5 friends, pick 3 to sit left-to-right on a bench. “Number of arrangements =
P(5,3) = 5×4×3 = 60
.”
True
False
6) Ice cream: Choose 2 flavors from 5 for a double scoop (order doesn’t matter). “Choices =
C(5,2) = 10
.”
True
False
7) Courses: You must pick 2 electives from 8 (order doesn’t matter). “Ways =
P(8,2) = 56
.”
True
False
8) Club IDs: 4-letter ID from A–Z with no repeated letters. “Number of IDs =
26×25×24×23 = 358,800
.”
True
False
9) Intramural teams: 20 students form 4-person teams (order doesn’t matter). “Number of distinct teams =
C(20,4) = 4,845
.”
True
False
10) Café: Pick 1 entrée (4 options), 1 side (5), 1 drink (3). “Total combos =
4×5×3 = 62
.”
True
False