# Binomial Coefficient - Factorials Part III

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## Homework Statement

##| \ X \in \mathcal P(\{0,1,2,3,4,5,6,7,8,9\}) : |X|= 4 \ | = \ \ ???##

## Homework Equations

There's no wording in the exercise , just what I wrote above.If I understood correctly , they asked me to find the cardinality of the set of all subsets of {0,1,2,3,4,5,6,7,8,9} that contains 4 elements.

So ##\binom{10}{4} = \frac{10!}{4!6!} = \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{4!6!} = \frac{10 \cdot 9 \cdot 8 \cdot 7}{4!} = \frac{5040}{24} = 210##

So there's 210 elements in ##\{X \in \mathcal P(\{0,1,2,3,4,5,6,7,8,9\}) : |X|= 4\}##

thought on this???

thank you!!

Last edited:

LCKurtz