How do you calculate how many possible combinations?Asked by: Amy Adams | Last update: 18 June 2021
Score: 4.1/5 (3 votes)
Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time.View full answer
Additionally, How do you calculate the number of possible combinations?
The formula for combinations is generally n! / (r! (n -- r)!), where n is the total number of possibilities to start and r is the number of selections made.
Also question is, How many combinations of 4 items are there?. I.e. there are 4 objects, so the total number of possible combinations that they can be arranged in is 4! = 4 x 3 x 2 x 1 = 24.
Similarly, How many combinations of 100 items are there?
It's fairly straightforward to calculate the number of combinations of a given set of n elements, taken k at a time. Given 100, choose 100, there is only one combination. Given 100, choose 99, there are 100 combinations. Given 100, choose 98, there are 161,700 combinations.
How many combinations of 20 items are there?
The number of combinations that are possible with 20 numbers is 1,048,575.
7*6*5=210. So you get 7∗6∗53∗2∗1 7 ∗ 6 ∗ 5 3 ∗ 2 ∗ 1 = 35 ways.
How many different ways can the letters P, Q, R, S be arranged? The answer is 4! = 24. The first space can be filled by any one of the four letters.
Explanation: If we are looking at the number of numbers we can create using the numbers 1, 2, 3, and 4, we can calculate that the following way: for each digit (thousands, hundreds, tens, ones), we have 4 choices of numbers. And so we can create 4×4×4×4=44=256 numbers.
In total you will find 5 × 24 = 120 possibilities.
One could say that a permutation is an ordered combination. The number of permutations of n objects taken r at a time is determined by the following formula: P(n,r)=n! (n−r)!
In your case, with 12 numbers, the number is 12x11x10x... x2x1=479001600. This number is called "twelve factorial" and written 12!, so, for example 4!= 4x3x2x1=24.
There are, you see, 3 x 2 x 1 = 6 possible ways of arranging the three digits. Therefore in that set of 720 possibilities, each unique combination of three digits is represented 6 times. So we just divide by 6. 720 / 6 = 120.
That is a total of 7 combinations.
For any group of 6 numbers and letters, there are a possible 720 different permutations or combinations that can be made.
The number of combinations that are possible with 10 numbers is 1,023.
A five-letter word with no repeated letters has 5! = 120 distinct arrangements.
Note: 8 items have a total of 40,320 different combinations.
How many Ways to Arrange 10 Letters Word STATISTICS? 50400 is the number of ways to arrange 10 letters (alphabets) word "STATISTICS" by using Permutations (nPr) formula.
= 5*4*3*2*1 = 120. Therefore, the number of ways in which the 3 letters can be arranged, taken all a time, is 3! = 3*2*1 = 6 ways.