Consider three boxes, each containing 10 balls labelled 1, 2, …,10. Suppose one ball is randomly drawn from each of the boxes. Denote by `n_(i)`,the label of the ball drawn from the `i^(th)` box, `(i=1,2,3)`. Then, the number of ways in which the balls can be chosen such that `n_(1) lt n_(2) lt n_(3)` is :

The number of ways in which n distinct balls can be put into three boxes, is

A box contains 10 white, 6 red and 10 black balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either white or red?

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3,4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let x_i be the number on the card drawn from the ith box, i = 1, 2, 3. The probability that x_1+x_2+x_3 is odd is

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3,4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let x_i be the number on the card drawn from the ith box, i = 1, 2, 3. The probability that x_1, x_2, x_3 are in an aritmetic progression is

A bag contains 20 balls numbered from 1 to 20 . One ball is drawn at random from the bag. What is the probability that the ball drawn is marked with a number which is multiple of 3 or 4 ?

A box contains 20 identical balls of which 10 balls are red . The balls are drawn at random from the box oone at a time with replacement .The probability that a white ball is drawn for the 4th time on the 7th draw is

There are two bags each of which contains n balls. A man has to select an equal number of balls from both the bags. Prove that the number of ways in which a man can choose at least one ball from each bag is ^(2n)C_n-1.

There are 6 balls of different colours and 3 boxes of different sizes. Each box can hold all the 6 balls. The balls are put in the boxes so that no box remains expty. The number of ways in which this can be done is (A) 534 (B) 543 (C) 540 (D) 28

Three boxes are labeled as A, B and C and each box contains 5 balls numbered 1, 2, 3, 4 and 5. The balls in each box are well mixed and one ball is chosen at random from each of the 3 boxes. If alpha, beta and gamma are the number on the ball from the boxes A, B and C respectively, then the probability that alpha=beta+gamma is equal to

A ball is drawn at random from a box containing 12 white, 16 red and 20 green balls. Determine the probability that the ball drawn is: (i) white