Out of $7$ consonants and $4$ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2$ vowels, is

In how many ways can a team of $10$ players be selected from $22$ players if $6$ particular players are always to be included and $4$ particular players are always excluded?

Number of ways of arranging $8$ identical books into $4$ identical shelves where any number of shelves may remain empty is equal to

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

If a question paper consists of $11$ questions divided into two sections,$I$ and $II$. Section $I$ consists of $6$ questions and section $II$ consists of $5$ questions,then the number of different ways a student can select $6$ questions,taking at least $2$ questions from each section,is

There are $15$ players in a cricket team,out of which $6$ are bowlers,$7$ are batsmen,and $2$ are wicketkeepers. The number of ways a team of $11$ players can be selected from them so as to include at least $4$ bowlers,$5$ batsmen,and $1$ wicketkeeper is $.....$