Find The Unknown In Each Item. 7. C(n, 2) = 78

answered • expert verified Find the unknown in each item. 7. C(n, 2) = 78 See answer Brainly User Brainly User

Answer:

To solve for the C(n, 2) = 78,  refer to the following:

• n! / r! (n - r)! = x
• n! / 2! (n - 2)! = 78
• n! (n - 2)! = 2! * 78
• n = 13

Combination

A combination could be a choice of all or a part of a collection of objects. The order of the chosen set is irrelevant. An example includes having a set of three letters: X, Y, and Z. We are looking for the number of ways we can select 2 letters from that set. A combination would be each possible selection. The complete list of possible selections would be: XZ XY, and YZ.

The number of tentative combinations of n objects taken r at a time is:

nCr = n(n - 1)(n - 2) ... (n - r + 1)/r! = n! / r!(n - r)! = nPr / r!

Note that XY and YX are considered to be one combination, because the order in which objects are selected does not matter. This is the key distinction between them and a permutation. A combination focuses on the choice of objects, order is irrelevant. A permutation, in distinction, focuses on the arrangement of objects with relevance regarding the order in which they're organized.

Types of combination

1. Repetition
2. No repetition

Repetition

In a combination, a repetition is referred to as having the same numbers in a set

No repetition

In a combination, no repetition means that no numbers should be repeated. The numbers are drawn one at a time. The order does not matter.

Examples of combination

1. Combination: Picking a team of 5 people from a group of 10
2. Combination: Choosing 8 desserts from a menu of 10.

For additional information regarding the combination of numbers, refer to the following links:

Number of possible combinations in a lotto

brainly.ph/question/1130922

Formula of combination

brainly.ph/question/499331

Further examples of combination

brainly.ph/question/499810

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