Counting
There are 11 runners in a race. In how many ways can the gold, silver, and bronze medals be awarded?
990
How many numbers between 1 and 120 (including both) are divisible by 2 or 3?
80
How many numbers are in the list:
-4, -3, -2,..., 15
20
A fair coin is tossed three times. What is the probability that at least one toss shows heads?
7/8
In how many ways can 6 students line up if Summer must stand in front of Robin (not necessarily right next to each other)?
360
We call a 3-digit PIN weak if any of its digits are the same. How many weak 3-digit PINs can be made?
280
How many numbers are in the list:
0, 1, 4, 9, 16, ..., 10000
101
Adam and Karim each roll one fair six-sided die. What is the probability that Adam’s roll is strictly greater than Karim’s?
5/12
How many different ways can you arrange the letters in AABCDE so that the letter B is always between two A’s? (Example: ACBDEA)
120
At a UN meeting with 80 delegates, each delegate speaks at least one of the following three languages: Arabic, English, and French.
- 35 delegates speak Arabic,
- 45 speak English,
- 25 speak French,
- 4 speak all three languages.
How many delegates speak exactly two of the three languages?
17
How many numbers are in the list:
1/2, 5/8, 3/4, 7/8, ..., 5
37
From a deck of 52 playing cards, Hamza picks 3 cards at random. What is the probability that all three cards are of the same rank (same number or same face)?
1/425 (or 6/2550 )