In Maricopa County, 5 persons are to be elected to the Board of Supervisors. If 8 persons are candidates, how many different arrangements are possible?
We want 8 choose 5, or 8C5. Typing this into the search engine we get 56.
license plate with 4 letter combinations and 3 number combinations
There are 26 total letters and 10 digits [0-9].
We have 26 C 4 * 10 C 3.
26 C 4 = 14,950
10 C 3 = 120
Total license plate combinations:
14,950 * 120 = 1,794,000
How many distinct 3 letter arrangements can be made using P, R, I, M and E?
We have all unique letters. We want the combination formula 5 Choose 3, or C(5,3).
Using our combinations calculator, we get 10 unique 3 letter arrangements.
Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are to be taken from the first 5 letters of the alphabet with repeats possible and the numbers are taken from the digits 0 through 9 with no repeats, how many serial numbers can be generated?
First 5...
Vanessa is packing her bags for her vacation. She has 5 unique action figures, but only 3 fit in her bag. How many different groups of 3 action figures can she take?
The key word here is different. This means combinations.
We use our combinations calculator to find 5 C 3 which equals 10.
Find the number of combinations and the number of permutations for 10 objects taken 6 at a time
Combinations is written as 10 C 6. Using our combinations calculator, we get 210.
Permutations is written as 10 P 6. Using our permutations calculator, we get 151,200.
There are 6 women and 5 men in a department. How many ways can a committee of 2 women and 2 men be selected?
We want 6C2 * 5C2 using combinations.
Using our combinations calculator, 6C2 = 15
Using our combinations calculator, 5C2 = 10
Our answer is 15 * 10 = 150
In how many ways can a committee consisting of 4 faculty members and 5 students be formed if there are 8 faculty members and 9 students eligible to serve on the committee?
We have 8 choose 4 * 9 choose 5 written as : 8C4 * 9C5
8C4 = 70
9C5 = 126
Multiply these together to get 8,820
The coach of a hockey team is holding tryouts and can take only 2 more players for the team. There are 5 players trying out. How many different groups of 2 players could possibly be chosen?
We want 5C2. Using our combinations calculator, we get:
10 possible combinations of 2 player groups
A small acting club has 8 members. How many different 2 member groups are possible?
We want 8C2
Using our combinations calculator, we get:
28 possible groups
From a standard 52 card deck, how many 6-card hands will have 2 spades and 4 hearts?
We want the product of 13C2 * 13C4 since we have 13 possible spades choose 2 and 13 possible hearts choose 4
Spades: 13C2 from our combinations calculator = 78
Hearts: 13C4 from our combinations calculator =...
CCP Stat Club is sending a delegate of 2 members to attend the 2015 Joint Statistical Meeting in Seattle. There are 10 qualified candidates. How many different ways can the delegate be selected?
10C2 = 45 shown on our Combinations Calculator
A professor wanted to test all possible pairwise comparisons among six means. How many comparisons did he need to compare?
a. 5
b. 6
c. 10
d. 15
d. 15 using our combinations calculator
How many ways can 4 trucks and 5 cars be selected from 15 cars and 12 trucks for a safety study?
We have Truck combinations * Car combinations:
12C4 * 15C5
495 * 3,003
1,486,485
We use the combination formula, 6 choose 5, or 6C5.
Using our combinations calculator, or entering 6C6 into the search engine, we get
6 ways to select.