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Mastering
AMC 8

Complementary Counting: all problems

Focus mode: every practice problem from the chapter, one after another.

0 / 15 solved

Problem 6.3.1

If you toss four coins, in how many ways will there be at least 1 head?

Problem 6.3.2

If you toss four coins, in how many ways will there be at least 2 heads?

Problem 6.3.3

How many three digit numbers contain the digit 5 at least once?

Problem 6.3.4

How many 3 digit numbers have at least 2 digits that are the same?

Problem 6.3.5

How many ways are there to select a group of 3 people from 5 women and 3 men if there must be at least 1 man in the group?

Problem 6.3.6

AMC 8

A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?

Problem 6.3.7

How many 4 digit numbers are not palindromes? A palindrome is a number that reads the same forward and backward.

Problem 6.3.8

Omega Learn Math Contest

Alice, Bob, Claire, Dave, Emma are sitting around a round table. Alice refuses to sit next to Bob. How many different ways can they sit around the table? (Rotations of the same arrangement are not considered different).

Problem 6.3.9

AMC 8

From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also a side of the octagon?

Problem 6.3.10

AMC 12

How many subsets of {2,3,4,5,6,7,8,9}\{2, 3, 4, 5, 6, 7, 8, 9\} contain at least one prime number?

Problem 6.3.11

There are 9 different flavors of ice cream at an ice cream shop. Joe wants to buy 2 or 3 scoops of different ice cream flavors. He doesn't like 2 of the flavors Mango and Chocolate together so won't buy them together. How many ways can he buy ice cream?

Problem 6.3.12(additional)

AMC 10

Una rolls 6 standard 6-sided dice simultaneously and calculates the product of the 6 numbers obtained. What is the probability that the product is divisible by 4?

Problem 6.3.13(additional)

AMC 8

Zara has a collection of 4 marbles: an Aggie, a Bumblebee, a Steelie, and a Tiger. She wants to display them in a row on a shelf, but does not want to put the Steelie and the Tiger next to one another. In how many ways can she do this?

Problem 6.3.14(additional)

There are 10 slips of paper numbered 1 to 5 in a bag, each equally likely to be drawn. You draw a slip, and then immediately put it back in the bag. What is the least number of slips you must draw in order to have at least a 12\frac12 chance of drawing the number 3?

Problem 6.3.15(additional)

You have 6 identical pears and 5 identical apples. You choose 4 fruits at random. What is the probability of picking at least 1 pear?