If $\binom{15}{3r} = \binom{15}{r+3}$,then $r = \dots$

The number of ways in which $6$ distinct things can be distributed into $2$ boxes so that no box is empty is

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these do the four cards belong to four different suits?

There are two urns. Urn $A$ contains $3$ distinct red balls,and Urn $B$ contains $9$ blue balls. If two balls are selected at random from each urn and swapped,in how many ways can this operation be performed?

The English alphabet has $5$ vowels and $21$ consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?

There are $15$ people at a party and each person shakes hands with every other person. What is the total number of handshakes?