Formulas and Pascal's Triangle
Permutations
Combinations
Probability
Mixed Bag
100
What formula should you use when you need to select r items from n available distinct items?
nCr
100
In how many different ways can 9 floats line up for a parade?
9!
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
362,880
100
The game euchre uses only 24 cards. How many 5-card hands can be made in the game?
24C5
=42,504
100
What is the probability that a 5-card Poker hand contains 5 hearts?
13C5/52C5
100
A box contains 12 dark-coloured and 8 light-coloured marbles. In how many different ways can you choose 3 dark marbles and 2 light marbles?
12C3 x 8C2
200
What is Row 3 of Pascal's triangle?
1 4 6 4 1
200
In how many different ways can 9 floats line up for a parade if the HWDSB float and the HWCDSB floats must go together?
8!2!
= 80,640
200
A customer can choose one of 4 different salad mixes, 3 of 8 different toppings, and one of 5 dressings. How many different salads can s/he create?
4C1x 8C3 x 5C1
160 different salads
200
What's the probability of cracking the 3-number code on a standard 60-number combination lock? 
1/(60x60x60)
= 1/216,000
= 0.0005 %
200
Your school yearbook has an editor-in-chief and an assistant editor-in-chief. If the yearbook staff has 15 members, in how many different ways can these positions be filled?
15P2
15 x 14
300
What formula should you use when you need to arrange r items out of n available distinct items?
nPr
300
In how many different ways can 9 floats line up for a parade if the HWDSB float and the HWCDSB floats must NOT go together?
9! - 8!2!
=282,240
300
In how many different ways can you answer a 14 question true or false quiz?
2^14
2x2x2x2x2x2x2x2x2x2x2x2x2x2
16,384
300
A lottery ticket contains five numbers chosen from the numbers 1 to 40. The winning ticket is the one that matches all five numbers, in any order. What's the probability of winning?
1 / 40C5
300
A video store receives 11 new movie posters. The store manager only has wall space for 4 posters. In how many ways can the manager arrange the posters?
11 P 4
400
What is the 41st term in the 43rd row of Pascal's Triangle?
43C41
=903
400
In a certain province, the license plate is made up of 3 letters followed by 4 numbers. If the letters may not be used more than once, and the first number must be greater than 5, but any number can be reused, how many different license plates are possible?
26 x 25 x 24 x 4 x 10 x 10 x 10
62,400,000
400
How many 5-card Poker hands contain 3 kings?
4C3 x 48C2
=4,512
400
Adrian has 15 classmates. He selects four of them to form a study group. What is the probability that Reg or Carlos is selected?
13C2/15C4
400
In a bag of marbles, there are 5 red marbles labeled 1 through 5 and 8 blue marbles labeled 1 through 8. You pull out one marble. What is the probability that you draw a red marble or an even numbered marble?
5/13 + 6/13 - 2/13 = 9/13
500
What formula do you use for rearranging objects, when some of them are identical?
n!/(p!q!)
500
In how many ways can you arrange the letters in the name John Phillip Sousa?
16! / 2!2!2!2!2!2!
500
The math department can buy up to 4 boxes of pens, up to 10 pads of paper, and up to 5 calculators without having to submit a request first. How many different supply orders are possible?
(4+1)(10+1)(5+1) - 1
= 329
500
A four-member curling team is randomly chosen from six grade 11 students and nine grade 12 students. What is the probability that the team has at least one grade 11 student?
1 - 9C4/15C4
500
In a bag of marbles, there are 5 red marbles labeled 1 through 5, and 8 blue marbles labeled 1 through 8. You draw two marbles without replacement. What is the probability that you draw a blue, odd-numbered marble first and that you draw a red marble next?
(4/13) x (5/12) = 5/39 = 12.8%