# Combinations - PowerPoint PPT Presentation

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Combinations. The combination key (nCr) is located under the math probability menu. Enter the number of objects, n, first; then the combination key; then the number of objects to take at one time, r. C(10,5) = 10C5 = 10 MATH PRB 3 5. Combination.

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Combinations

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### Combinations

• The combination key (nCr) is located under the math probability menu. Enter the number of objects, n, first; then the combination key; then the number of objects to take at one time, r.

• C(10,5) = 10C5 = 10 MATH PRB 3 5

### Combination

• Sometimes, combinations need combined with the fundamental counting principle. This can easily be done one the calculator.

• Example: How many ways can five women be selected from ten women and three men selected from eight men? The solution is shown below. The parentheses are optional, but it is suggested you use them for clarification

• ( 10 nCr 5 ) * ( 8 nCr 3 )

### Factorials

• The factorial (!) key is located under the math probability menu. Enter the number first, then the factorial key.

• 10! = 10 MATH PRB 4

### Factorial

• factorial notation: the notation, n!, used to represent the product of the first n natural numbers. n! is read as “n factorial.”

• For example,

• n! = n × (n - 1) × (n - 2) × (n - 3) × ... × 3 × 2 × 1

• Note: By definition, 0! = 1. Another thing you must remember is that n! is only defined if n is a whole number. This means numbers like 1.5! and (-2)! are undefined.

• Principle: The number of distinguishable permutations of n objects, of which a objects are identical, another b objects are identical, and another c objects are identical, and so on, is

### Factorial

• Note: By definition, 0! = 1. Another thing you must remember is that n! is only defined if n is a whole number. This means numbers like 1.5! and (-2)! are undefined.

• Principle: The number of distinguishable permutations of n objects, of which a objects are identical, another b objects are identical, and another c objects are identical, and so on, is