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43 votes
43 votes
Suppose we want to choose 7 letters, without replacement, from 12 distinct letters. (a) How many ways can this be done, if the order of the choices is not relevant?

User Databyte
by
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2 Answers

23 votes
23 votes

Answer:

3991680 or 792

Explanation:

12P7 = 3991680

or

12C7 = 792

P = permutation

C = combination

Sorry, I am not sure which answer is correct or if any of the answers are correct.

User Rsantiago
by
2.6k points
14 votes
14 votes

In order to find out the number of ways 7 letters can be selected from 12 letters, when order is not important, we can use the concept of combinations from combinatorial mathematics.

The formula for combinations is given as follows:

C(n, r) = n! / [(n - r)! * r!]

Here,
- n (total_letters) is the total number of elements from which elements will be chosen;
- r (letters_chosen) is the number of elements that are to be chosen;
- C(n, r) represents the number of combinations;
- "!" denotes the factorial of a number.

Let's calculate the combination:

First, let's plug the numbers into the formula:

C(12, 7) = 12! / [(12 - 7)! * 7!]

The factorial of a number is the product of that number and all the numbers below it down to 1. So here, we calculate the factorials:

- 12! equals 479,001,600
- 7! equals 5,040
- (12 - 7)! equals 5!

So we substitute these values into the formula:

C(12, 7) = 479,001,600 / [(5!) * 5,040]

5! equals 120.

So, C(12,7) = 479,001,600 / [120 * 5,040]

Finally, divide the numerator by the denominator gives us the number of ways 7 letters can be selected from 12 different letters.

So, there are 792 ways 7 letters can be chosen from the 12 distinct letters, when order does not matter.

User Brad Rhoads
by
2.9k points
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