Howdy y'all! I'm Carl Manuel and I'm here to talk about COMBINATIONS!
A combination is an unordered collection of elements, unlike permutations where it is a collection of ordered elements. With a permutation, we select and order the elements (two actions). But with a combination, we only select the elements (one action). Must use the formula for a combination -- cannot use the dash method.
Example:
Permutation question
How many ways can 5 books be arranged on a shelf?
- Notice the word "arranged". Remember that combinations do not need to be arranged, hence making this question a permutation question.
Combination question
How many ways can you select two books to read on your holiday if there are 5 books to choose from?
- Words like select and choose are found in this question but it does not say to arrange so this question must be a combination question.
Formula for Combination
*must use all the time, no dash method*
Example question:
A student has a penny, a nickel, a dime, a quarter, and a half doller and wishes to leave a tip consisting of exactly 3 coins. How many different tips are possible?
r = 3 3! (5 - 3)! 3! 2! 3! 2!
NOTE: N C X = N C Y Mr. Piatek likes to put booby traps, keep that in mind.
N = X + Y You've been warned.
RECAP:
- Combinations is an unordered collection of elements
- MUST always use formula, cannot use dash method ever.
- Combinations are only selections, no arrangements like permutations.
- If nCx = nCy , you can add x and y together to find n. ( n = x + y )
- Always read the question thoroughly. Read it once and then read it one more time. Determine whether it is permutation or combination first and then find out what the question is looking for.
Good luck everyone! Remember, if we all ace our quizzes... donuts.
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