COMC Geometry and Combinatorics Flashcards
6 cards from real COMC practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 COMC Geometry and Combinatorics flashcards as text
In how many ways can 5 distinct books be arranged on a shelf?
Answer: 120
The number of permutations of 5 distinct objects is 5! = 5 × 4 × 3 × 2 × 1 = 120.
How many ways can a committee of 3 people be chosen from a group of 12?
Answer: 220
C(12,3) = 12!/(3!×9!) = (12×11×10)/(3×2×1) = 220.
How many 4-digit numbers can be formed using digits 1–9 without repetition?
Answer: 3024
This is P(9,4) = 9 × 8 × 7 × 6 = 3024 ordered arrangements.
If two fair six-sided dice are rolled, in how many ways can the sum equal 7?
Answer: 6
The pairs are (1,6),(2,5),(3,4),(4,3),(5,2),(6,1), giving exactly 6 ordered outcomes.
In how many ways can 8 people be split into two unlabeled groups of 4?
Answer: 35
Choose 4 people in C(8,4) = 70 ways, then divide by 2 because swapping the two groups gives the same split: 70/2 = 35.
How many distinct arrangements are there of the letters in the word LEVEL?
Answer: 30
LEVEL has 5 letters with L appearing twice and E appearing twice, giving 5!/(2!×2!) = 120/4 = 30.