combinations

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.