If $C(n, 7) = C(n, 5)$,find $n$.

The number of $5$ digit telephone numbers having at least one of their digits repeated is

$A$ parallelogram is cut by two sets of $m$ lines parallel to its sides. The number of parallelograms thus formed 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:

Six married couples decide to form a committee of $6$ persons. The total number of ways to form the committee such that it contains no couples is equal to:

In an examination,Yamini has to select $4$ questions from each part. There are $6, 7,$ and $8$ questions in Part-$I,$ Part-$II,$ and Part-$III,$ respectively. What is the number of possible combinations in which she can choose the questions?