From a group of $7$ men and $6$ women,five persons are to be selected to form a committee so that at least $3$ men are there on the committee. In how many ways can it be done?

How many numbers of five digits can be formed with the digits $0, 1, 2, 3, 5$ and $6$?

There are $m$ points on a straight line $AB$ and $n$ points on another line $AC$,none of them being the point $A$. Triangles are formed from these points as vertices when $(i)$ $A$ is excluded and $(ii)$ $A$ is included. Then the ratio of the number of triangles in the two cases is

If $\sum_{i=0}^4 {^{4+i}}C_i + \sum_{j=6}^9 {^{3+j}}C_j = {^x}C_y$ ($x$ is a prime number),then which one of the following is incorrect?

$A$ dictionary is printed consisting of $7$-letter words only that can be formed using the letters of the word $CRICKET$. If the words are arranged in alphabetical order,as in an ordinary dictionary,then the number of words before the word $CRICKET$ is:

Find how many words can be formed out of the letters of the word '$ORIENTAL$' so that vowels always occupy the odd places.