There are 20 cards. Ten of these cards have the letter `"I"` printed on them and the other 10 have the letter `"T"` printed on them. If three cards picked up at random and kept in the same order, the probability of making word IIT is

Five cards – the ten, jack, queen, king and ace of diamonds, are well shuffled with their face downwards. One card is then picked up at random. What is the probability that the card is the queen?

Once again you are given four cards. Each card has a number printed on one side and a letter on the other side. Which are the only two cards you need to turn over to check whether the following rule holds? "If a card has a consonant on one side, then it has an odd number on the other side."

A hat contains a number of cards with 30% white on both sides, 50% black on one side and whit e on the other side, 20% black on both sides. The cards are mixed up, and a single card is drawn at random and placed on the table. Its upper side shows up black. The probability that its other side is also black is

Five cards – the ten, jack, queen, king and ace of diamonds, are well shuffled with their face downwards. One card is then picked up at random.If the queen is drawn and put aside, what is the probability that the second card picked up is a queen?

In a bag there are 44 identical cards with figure of circle or square on them. There are 24 circles, of which 9 are blue and rest are green and 20 squares of which 11 are blue and rest are green. One card is drawn from the bag at random. Find the probability that it has the figure of square.

Let f(n) be the number of regions in which n coplanar circles can divide the plane. If it is known that each pair of circles intersect in two different points and no three of them have common points of intersection, then (i) f(20) = 382 (ii) f(n) is always an even number (iii) f^(-1)(92) = 10 (iv) f(n) can be odd

Five letter words, having distinct letters, are to be constructed using the letters of the word 'EQUATION' so that each word contains exactly three vowels and two consonants. How many of them have all the vowels together?

In how many ways can a pack of 52 cards divided in 4 sets, three of them having 17 cards each and fourth just 1 card ?