If $^{43}{C_{r - 6}} = {\,^{43}}{C_{3r + 1}},$ then the value of $r$ is
$12$
$8$
$6$
$10$
The number of four letter words that can be formed using the letters of the word $BARRACK$ is
In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman
It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?
Let $n(A) = 3, \,n(B) = 3$ (where $n(S)$ denotes number of elements in set $S$), then number of subsets of $(A \times B)$ having odd number of elements, is-
A student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first five questions. The number of choices available to him is