Words with or without meaning are to be formed using all the letters of the word $EXAMINATION.$ The probability that the letter $\mathrm{M}$ appears at the fourth position in any such word is:
$\frac{1}{9}$
$\frac{1}{66}$
$\frac{2}{11}$
$\frac{1}{11}$
A committee of two persons is selected from two men and two women. What is the probability that the committee will have no man ?
A committee of five is to be chosen from a group of $9$ people. The probability that a certain married couple will either serve together or not at all, is
A man draws a card from a pack of $52$ playing cards, replaces it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two times is
A basket contains $5$ apples and $7$ oranges and another basket contains $4$ apples and $8$ oranges. One fruit is picked out from each basket. Find the probability that the fruits are both apples or both oranges
If four vertices of a regular octagon are chosen at random, then the probability that the quadrilateral formed by them is a rectangle is