Hey kids. A
couple of days ago we learned how to do Combinations and I will try to repeat
the lesson here as good as Mr. P teaches.
Permutations
and Combinations may look similar, but have different concepts. One thing to
know is that permutations is an ordered collection of elements while a
combinations consists of unordered collection of elements.
Combination
Notation: C(n,r) or nCr which
is also n!
r! (n-r)!
Remember, we
cannot use the dash method for combinations and must only select the elements
(no ordering).
Here Is a
simple example with the formula: 10C2
*First we
write out the formula.
nCr = n! *then we substitute 10!
r!(n-r)! (n= 10, r=2) 2!(10-2)!
*We solve
the bracket in the denominator so, it equals
10!
*Now we must cancel the 8! by listing the integers down from 10 until we
reach 8
2!8!
= 10x9x8!
*cross out common integers
= 10x9!
2!8! 2!
*now you can
solve!
10x9
= 90 which is 45. We have our
answer! Yay!
2 2
Now, let’s
try it out with a word problem.
“A student has
a penny, a nickel, a dime, a quarter and a half dollar and wishes to leave a
tip consisting of exactly 3 coins. How many *different* tips are possible
nCr = n! n= 5, r=3 *n must be total number and r must
be how much is needed
r!(n-r)!
= 5! = 5!
3!(5-3)! 3!2!
= 5x4x3
*cancel out 3 = 5x4 = 10 And that’s basically how you use the
formula!!!
3!2! 2
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