Pearson Geometry Common Core, 2011
PG
Pearson Geometry Common Core, 2011 View details
4. Compound Probability
Continue to next subchapter

Exercise 33 Page 849

Is the order important?

15 600

Practice makes perfect
We want to find how many ways there are to make a letter sequence out of three different letters. Note that in this case, the order is important, meaning each possible arrangement is a permutation. To calculate the number of potential sequences, we will use the formula for permutations of n objects taken r at a time. _n P_r = n!/(n-r)! We have twenty six letters in the alphabet and are taking three at a time. This means that n is 26 and r is 3. Let's substitute 26 for n and 3 for r in the formula above.
_n P_r = n!/(n-r)!
_(26) P_3 = 26!/( 26- 3)!
â–Ľ
Simplify
_(26) P_3 = 26!/23!

Write as a product

_(26) P_3 = 26* 25* 24* 23!/23!
_(26) P_3 = 26* 25* 24/1
_(26) P_3 = 26* 25* 24
_(26) P_3 = 15 600
There are 15 600 permutations.