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
How many distinct arrangements are there of the letters in BANANA?
Answer: 60
6!/(3!·2!) = 720/12 = 60.
Two fair dice are rolled. What is the probability that the sum is 7?
Answer: 1/6
Six of the 36 outcomes sum to 7, giving 6/36 = 1/6.
How many ordered triples of nonnegative integers (x, y, z) satisfy x + y + z = 10?
Answer: 66
By stars and bars, C(12,2) = 66.
How many subsets of {1, 2, ..., 10}, including the empty set, contain no two consecutive integers?
Answer: 144
The count for {1..n} is the Fibonacci number F(n+2), and F(12) = 144.
How many permutations of 5 distinct letters leave no letter in its original position?
Answer: 44
The derangement number D5 = 5!(1 − 1 + 1/2 − 1/6 + 1/24 − 1/120) = 44.
A fair coin is flipped 6 times. What is the probability of getting exactly 3 heads?
Answer: 5/16
C(6,3)/2^6 = 20/64 = 5/16.
A committee of 3 is chosen from 5 men and 4 women. How many committees include at least one woman?
Answer: 74
Total C(9,3) = 84 minus all-men C(5,3) = 10 gives 74.
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