Six ‘$+$’ and four ‘$-$’ signs are to placed in a straight line so that no two ‘$-$’ signs come together, then the total number of ways are
$15$
$18$
$35$
$42$
There are $15$ persons in a party and each person shake hand with another, then total number of hand shakes is
If $^{2n}{C_2}{:^n}{C_2} = 9:2$ and $^n{C_r} = 10$, then $r = $
If $^n{C_r}$ denotes the number of combinations of $n$ things taken $r$ at a time, then the expression $^n{C_{r + 1}} + {\,^n}{C_{r - 1}} + \,2 \times {\,^n}{C_r}$ equals
For a scholarship, atmost $n$ candidates out of $2n+1$ can be selected. If the number of different ways of selection of atleast one candidate for scholarship is $63$, then maximum number of candidates that can be selected for the scholarship is -
In how many ways can $21$ English and $19$ Hindi books be placed in a row so that no two Hindi books are together