Combinatorics & Probability Flashcards

6 cards from real AMC12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Combinatorics & Probability flashcards as text

How many distinct arrangements exist of the letters in MISSISSIPPI?
Answer: 34650
11!/(1!4!4!2!)=39916800/1152=34650.
How many ways can 4 books be chosen from 10 if order does not matter?
Answer: 210
C(10,4)=10!/(4!6!)=210.
A committee of 3 is chosen from 5 men and 4 women. How many committees have exactly 2 women?
Answer: 30
C(4,2)*C(5,1)=6*5=30.
If P(A)=0.4 and P(B)=0.5 and A and B are independent, what is P(A and B)?
Answer: 0.2
For independent events, P(A and B)=P(A)*P(B)=0.4*0.5=0.2.
How many diagonals does a convex octagon have?
Answer: 20
Diagonals = n(n-3)/2 = 8*5/2 = 20.
A fair coin is flipped 4 times. What is the probability of exactly 2 heads?
Answer: 3/8
C(4,2)/2^4=6/16=3/8.