A father with $8$ children takes them $3$ at a time to the Zoological gardens, as often as he can without taking the same $3$ children together more than once. The number of times each child will go to the garden is
$56$
$21$
$112$
None of these
If the different permutations of all the letter of the word $\mathrm{EXAMINATION}$ are listed as in a dictionary, how many words are there in this list before the first word starting with $\mathrm{E}$ ?
In an election there are $5$ candidates and three vacancies. A voter can vote maximum to three candidates, then in how many ways can he vote
In how many ways can a girl and a boy be selected from a group of $15$ boys and $8 $ girls
If $^{43}{C_{r - 6}} = {\,^{43}}{C_{3r + 1}},$ then the value of $r$ is
Let the number of elements in sets $A$ and $B$ be five and two respectively. Then the number of subsets of $A \times B$ each having at least $3$ and at most $6$ element is :