- Statistics Tutorial
- Home
- Adjusted R-Squared
- Analysis of Variance
- Arithmetic Mean
- Arithmetic Median
- Arithmetic Mode
- Arithmetic Range
- Bar Graph
- Best Point Estimation
- Beta Distribution
- Binomial Distribution
- Black-Scholes model
- Boxplots
- Central limit theorem
- Chebyshev's Theorem
- Chi-squared Distribution
- Chi Squared table
- Circular Permutation
- Cluster sampling
- Cohen's kappa coefficient
- Combination
- Combination with replacement
- Comparing plots
- Continuous Uniform Distribution
- Continuous Series Arithmetic Mean
- Continuous Series Arithmetic Median
- Continuous Series Arithmetic Mode
- Cumulative Frequency
- Co-efficient of Variation
- Correlation Co-efficient
- Cumulative plots
- Cumulative Poisson Distribution
- Data collection
- Data collection - Questionaire Designing
- Data collection - Observation
- Data collection - Case Study Method
- Data Patterns
- Deciles Statistics
- Discrete Series Arithmetic Mean
- Discrete Series Arithmetic Median
- Discrete Series Arithmetic Mode
- Dot Plot
- Exponential distribution
- F distribution
- F Test Table
- Factorial
- Frequency Distribution
- Gamma Distribution
- Geometric Mean
- Geometric Probability Distribution
- Goodness of Fit
- Grand Mean
- Gumbel Distribution
- Harmonic Mean
- Harmonic Number
- Harmonic Resonance Frequency
- Histograms
- Hypergeometric Distribution
- Hypothesis testing
- Individual Series Arithmetic Mean
- Individual Series Arithmetic Median
- Individual Series Arithmetic Mode
- Interval Estimation
- Inverse Gamma Distribution
- Kolmogorov Smirnov Test
- Kurtosis
- Laplace Distribution
- Linear regression
- Log Gamma Distribution
- Logistic Regression
- Mcnemar Test
- Mean Deviation
- Means Difference
- Multinomial Distribution
- Negative Binomial Distribution
- Normal Distribution
- Odd and Even Permutation
- One Proportion Z Test
- Outlier Function
- Permutation
- Permutation with Replacement
- Pie Chart
- Poisson Distribution
- Pooled Variance (r)
- Power Calculator
- Probability
- Probability Additive Theorem
- Probability Multiplecative Theorem
- Probability Bayes Theorem
- Probability Density Function
- Process Capability (Cp) & Process Performance (Pp)
- Process Sigma
- Quadratic Regression Equation
- Qualitative Data Vs Quantitative Data
- Quartile Deviation
- Range Rule of Thumb
- Rayleigh Distribution
- Regression Intercept Confidence Interval
- Relative Standard Deviation
- Reliability Coefficient
- Required Sample Size
- Residual analysis
- Residual sum of squares
- Root Mean Square
- Sample planning
- Sampling methods
- Scatterplots
- Shannon Wiener Diversity Index
- Signal to Noise Ratio
- Simple random sampling
- Skewness
- Standard Deviation
- Standard Error ( SE )
- Standard normal table
- Statistical Significance
- Statistics Formulas
- Statistics Notation
- Stem and Leaf Plot
- Stratified sampling
- Student T Test
- Sum of Square
- T-Distribution Table
- Ti 83 Exponential Regression
- Transformations
- Trimmed Mean
- Type I & II Error
- Variance
- Venn Diagram
- Weak Law of Large Numbers
- Z table
- Statistics Useful Resources
- Statistics - Discussion
Statistics - Combination
A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected. For example, suppose we have a set of three letters: A, B, and C. we might ask how many ways we can select 2 letters from that set.
Combination is defined and given by the following function −
Formula
${C(n,r) = \frac{n!}{r!(n-r)!}}$
Where −
${n}$ = the number of objects to choose from.
${r}$ = the number of objects selected.
Example
Problem Statement −
How many different groups of 10 students can a teacher select from her classroom of 15 students?
Solution −
Step 1 − Determine whether the question pertains to permutations or combinations. Since changing the order of the selected students would not create a new group, this is a combinations problem.
Step 2 − Determine n and r
n = 15 since the teacher is choosing from 15 students.
r = 10 since the teacher is selecting 10 students.
Step 3 − Apply the formula
${^{15}C_{10} = \frac{15!}{(15-10)!10!} \\[7pt] = \frac{15!}{5!10!} \\[7pt] = \frac{15(14)(13)(12)(11)(10!)}{5!10!} \\[7pt] = \frac{15(14)(13)(12)(11)}{5!} \\[7pt] = \frac{15(14)(13)(12)(11)}{5(4)(3)(2)(1)} \\[7pt] = \frac{(14)(13)(3)(11)}{(2)(1)} \\[7pt] = (7)(13)(3)(11) \\[7pt] = 3003}$