In how many ways can $6$ persons stand in a queue at a time?

$A = \{ x_1, x_2, x_3, x_4 \}; \, B = \{ y_1, y_2, y_3, y_4 \}.$ $A$ function is defined from set $A$ to set $B.$ The number of one-one functions such that $f(x_i) \neq y_i$ for $i = 1, 2, 3, 4$ is equal to:

From a group of $7$ men and $6$ women,five persons are to be selected to form a committee so that at least $3$ men are there in the committee. In how many ways can it be done?

The value of $\sum_{r=0}^{20} {}^{50-r}C_{6}$ is equal to

Total number of $6$-digit numbers in which only and all the five digits $1, 3, 5, 7,$ and $9$ appear,is

$n$-digit numbers are formed using only three digits $2, 5$,and $7$. The smallest value of $n$ for which $900$ such distinct numbers can be formed is: