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
$15$
$18$
$35$
$42$
The number of ways in which four letters of the word $‘MATHEMATICS$’ can be arranged is given by
The number of ways in which any four letters can be selected from the word ‘$CORGOO$’ is
If ${ }^{n} P_{r}={ }^{n} P_{r+1}$ and ${ }^{n} C_{r}={ }^{n} C_{r-1}$, then the value of $r$ is equal to:
If $^n{C_3} + {\,^n}{C_4} > {\,^{n + 1}}{C_3},$ then
The number of four-letter words that can be formed with letters $a, b, c$ such that all three letters occur is