Let him invite $r$ friends at a time in each party.

Then the number of parties = $^{10}C_r$

This is maximum only if $r=5$

Out of these $ ^{10}C_5$ parties a particular person can be found in

$^9C_4 =126$ parties.

This is because out of any 5 friends 1 particular friend is included and the

remaining 4 friends are to be selected from remaining 9 friends.=$^9C_4$ (ways.)