There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84,$ then the value of $m$ is
$12$
$11$
$9$
$7$
In a club election the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote be $62,$ then the number of candidates is :-
If $^{n} C _{9}=\,\,^{n} C _{8},$ find $^{n} C _{17}$
The number of ways in which four letters of the word $‘MATHEMATICS$’ can be arranged is given by
Find the number of ways of selecting $9$ balls from $6$ red balls, $5$ white balls and $5$ blue balls if each selection consists of $3$ balls of each colour.
How many words, with or without meaning, each of $3$ vowels and $2$ consonants can be formed from the letters of the word $INVOLUTE$?