If $n$ and $r$ are two positive integers such that $n \ge r,$ then $^n{C_{r - 1}}$$ + {\,^n}{C_r} = $
$^n{C_{n - r}}$
$^n{C_r}$
$^{n - 1}{C_r}$
$^{n + 1}{C_r}$
If $^{43}{C_{r - 6}} = {\,^{43}}{C_{3r + 1}},$ then the value of $r$ is
The value of $\sum \limits_{ r =0}^{20}{ }^{50- r } C _{6}$ is equal to
If $^n{P_r}$=$ 720$.$^n{C_r},$ then $r$ is equal to
$^n{C_r}{ + ^n}{C_{r - 1}}$ is equal to
A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:
at most $3$ girls?