Andhra Pradesh Board Solutions for Exercise 5: Exercise 5(e)

If ${}^{n}C_4=210$, find $n$.

If ${}^{12}\mathrm{C}_{\mathrm{r}}=495$, find the possible values of '$r$'

If $10.{}^n\mathrm{C}_2=3{.}^{n+1}{\mathrm{C}}_3$, find $n$

Find the number of ways of forming a committee of $5$ members out of $6$ Indians and $5$ Americans so that always the Indians will be in majority in the committee.

A question paper is divided into $3$ sections $A,B,C$ containing $3,4,5$ questions  respectively. Find the number of ways of attempting $6$ questions choosing at least one from each section.

Find the number of ways in which $12$ things be divided into $4$ equal groups.

The number of ways in which $12$ things be divided to $4$ persons equally is $\frac{k!}{(3!{)}^4}$,then find the value of $k$

A class contains $4$ boys and $g$ girls. Every Sunday, five students with at least $3$ boys go for a picnic. A different group is being sent every week. During the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed is $85$, find $g$.