$A$ student has to answer $10$ out of $13$ questions in an examination,choosing at least $5$ questions from the first $6$ questions. The number of choices available to the student is:

In how many ways can one girl and one boy be selected from a group of $15$ boys and $8$ girls?

$A$ linguistic club of a certain Institute consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this group,including the selection of a Captain (from among these $4$ members) for the team. If the team has to include at most one boy,the number of ways of selecting the team is:

$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times each child will go to the garden is

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

From $5$ consonants and $5$ vowels,how many words can be formed using $3$ consonants and $2$ vowels?