Questions like this are answered by the binomial coefficient. The binomial coefficient [tex] \binom{n}{k} [/tex] (read "n choose k") means exactly what you're looking for: "How many ways are there to choose k elements from a set of n elements?"
In other words, it counts the number of possible subsets of cardinality k from a set of cardinality n. It is defined as follows:
[tex] \displaystyle \binom{n}{k} = \dfrac{n!}{k!(n-k)!} [/tex]
Where n! is the factorial of n:
[tex] n! = n(n-1)(n-2)(n-3)\ldots 4 \cdot 3 \cdot 2 [/tex]
So, you have
[tex] \displaystyle \binom{14}{9} = \dfrac{14!}{9!5!} = \dfrac{14\cdot13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2}{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot5\cdot4\cdot3\cdot2} [/tex]
Of course, a lot of factors simplify:
[tex] \dfrac{14!}{9!5!} = \dfrac{14\cdot13\cdot12\cdot11\cdot10}{5\cdot4\cdot3\cdot2} = 14\cdot13\cdot11 = 2002 [/tex]
Answer:
iiiiiiiiiiiiii am not sure 69 maybe
Step-by-step explanation:
