The sum of all three-digit numbers,formed using non-zero digits,where all the digits are perfect squares of a natural number,is:

The number of ways in which the following prizes can be given to a class of $20$ boys,first and second Mathematics,first and second Physics,first Chemistry,and first English is:

$A = \{ x_1, x_2, x_3, x_4 \}; \, B = \{ y_1, y_2, y_3, y_4 \}.$ $A$ 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:

If $P(56, r+6) : P(54, r+3) = 30800 : 1$,find $r$.

From $8$ men and $6$ women,a group of seven persons is to be formed. In how many ways can the group be formed such that the group includes at least two ladies?

There are $3$ candidates for a post and one is to be selected by the votes of $7$ men. The number of ways in which votes can be given is