What's 10P5? What's 9C3?

P_(10,5)=30,240; C_(9,3)=84

Explanation:

${P}_{10 , 5}$

This is the permutation of a population of 10, choosing 5. The general formula for a permutation is:

P_(n,k)=(n!)/((n-k)!); n="population", k="picks"

P_(10,5)=(10!)/((10-5)!)=(10!)/(5!)=>

$10 \times 9 \times 8 \times 7 \times 6 = 30 , 240$

${C}_{9 , 3}$

This is the combination of a population of 9, choosing 3. The general formula for a combination is:

C_(n,k)=(n!)/((k)!(n-k)!) with $n = \text{population", k="picks}$

C_(9,3)=(9!)/((3)!(9-3)!)=(9!)/((3!)(6!))=>

(cancel9^3xxcancel8^4xx7xxcancel(6!))/(cancel3xxcancel2xxcancel(6!))=3xx4xx7=84