AMC12 Combinatorics & Probability 2 — Questions and Answers
Question 1: How many distinct arrangements exist of the letters in MISSISSIPPI?
- 11520
- 5040
- 27720
- 34650 (Correct answer)
Correct answer: 34650
11!/(1!4!4!2!)=39916800/1152=34650.
Question 2: How many ways can 4 books be chosen from 10 if order does not matter?
- 5040
- 120
- 840
- 210 (Correct answer)
Correct answer: 210
C(10,4)=10!/(4!6!)=210.
Question 3: A committee of 3 is chosen from 5 men and 4 women. How many committees have exactly 2 women?
- 18
- 24
- 60
- 30 (Correct answer)
Correct answer: 30
C(4,2)*C(5,1)=6*5=30.
Question 4: If P(A)=0.4 and P(B)=0.5 and A and B are independent, what is P(A and B)?
- 0.9
- 0.1
- 0.45
- 0.2 (Correct answer)
Correct answer: 0.2
For independent events, P(A and B)=P(A)*P(B)=0.4*0.5=0.2.
Question 5: How many diagonals does a convex octagon have?
- 28
- 16
- 12
- 20 (Correct answer)
Correct answer: 20
Diagonals = n(n-3)/2 = 8*5/2 = 20.
Question 6: A fair coin is flipped 4 times. What is the probability of exactly 2 heads?
- 1/4
- 1/2
- 5/16
- 3/8 (Correct answer)
Correct answer: 3/8
C(4,2)/2^4=6/16=3/8.
AMC12 Combinatorics & Probability 2
How many distinct arrangements exist of the letters in MISSISSIPPI?