Combinatorics & Probability Flashcards
7 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Combinatorics & Probability flashcards as text
What is the expected number of rolls of a fair six-sided die needed to roll the first 6?
Answer: 6
The number of trials until the first success is geometric with mean 1/p = 6.
How many lattice paths go from (0,0) to (4,3) using only unit steps right or up?
Answer: 35
Choose which 3 of the 7 steps are up: C(7,3) = 35.
In how many ways can 6 people be seated around a round table if rotations are considered the same?
Answer: 120
Circular arrangements of n people number (n−1)! = 5! = 120.
Two cards are drawn without replacement from a standard 52-card deck. What is the probability that both are aces?
Answer: 1/221
(4/52)(3/51) = 12/2652 = 1/221.
How many integers from 1 to 100 are divisible by 2, 3, or 5?
Answer: 74
Inclusion-exclusion: 50+33+20−16−10−6+3 = 74.
How many diagonals does a convex decagon have?
Answer: 35
A convex n-gon has n(n−3)/2 diagonals, so 10·7/2 = 35.
Three fair dice are rolled. What is the probability that all three show different numbers?
Answer: 5/9
(6·5·4)/216 = 120/216 = 5/9.
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