$\binom{n}{r} \div \binom{n}{n-1} = \dots$

There are $12$ volleyball players in total in a college,out of which a team of $9$ players is to be formed. If the captain always remains the same,in how many ways can the team be formed?

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn,two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

The number of $4$-letter words,with or without meaning,each consisting of $2$ vowels and $2$ consonants,which can be formed from the letters of the word $UNIVERSE$ without repetition is $.........$.

The number of ways in which one or more balls can be selected out of $10$ white,$9$ green,and $7$ blue balls is:

If $^{n + 1}C_3 = 2 \cdot ^nC_2$,then $n =$