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We find the formula for the maximal cardinality of the family of $n$-tuplesfrom ${[n]\choose k}$ with does not have $\ell$--matching. This formula aftersome analytical issues can be reduce to the Erd\"os's Matching formula. Also weprove the conjecture about the cardinality of maximal $s$-wise $t$-intersectingfamily of $k$-element subsets of $[n]$. In the proofs we use original methodwhich we have already used in the proof of Mikl\'os-Manikam-Singhi conjecturein \cite{1}. We call this method Symmetrical smoothing method

Erd\"os's Matching Conjecture and $s$-wise $t$-intersection Conjecture via Symmetrical Smoothing Method