AMC12 Combinatorics & Probability 2

Question 1

How many distinct arrangements exist of the letters in MISSISSIPPI?

Accepted Answer

34650

Answer

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?

Accepted Answer

210

Answer

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?

Accepted Answer

30

Answer

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)?

Accepted Answer

0.2

Answer

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?

Accepted Answer

20

Answer

Diagonals = n(n-3)/2 = 8*5/2 = 20.

AMC12 - American Mathematics Competition 12 Practice Test