if the number of subsets with 4 elements of a set A is equal to the number of subsets with 5 elements of the set, then the number of subsets with 3 elements of this set is ?

Question

goformit100 · Answer

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anonymous · Answer

Suppose: $$
\|A\| = n
$$

anonymous · Answer

if the number of subsets with 4 elements of a set A is equal to the number of subsets with 5 elements of the set$$
\binom{n}{4}=\binom{n}{5}
$$

then the number of subsets with 3 elements of this set is$$
\binom{n}{3}=x
$$

anonymous · Answer

Solve for $n$, then solve for $x$.

anonymous · Answer

$$
\binom{n}{k}\iff ^nC_k\iff (n\text{ choose }k)
$$

anonymous · Answer

$$
\binom nk=\frac{n!}{k!(n-k)!}
$$

anonymous · Answer

@MissKhan What more must I do to get this medal?!

anonymous · Answer

@wio  How should i award you the medal ? sorry am new at this

anonymous · Answer

Click best response.