Seven people leave their bags outside al temple and returning after worshiping picked one bag each at random. In how many ways at least one and at most three of them get their correct bags?

A bag contains 12 pairs of socks. Four socks are picked up at random. Find the probability that there is at least one pair.

In how many ways 14 identical toys be distributed among three boys so that each one gets atleast one toy and no two boys get equal no of toys ?

A bag contains a white and b black balls. Two players, Aa n dB alternately draw a ball from the bag, replacing the ball each time after the draw till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B , then find the ratio a : b

(i) In how many ways can a pack of 52 cards be divided equally among four players? (ii) In how many ways can you divide these cards in four sets, three of them having 17 cards each and the fourth one just one card?

A bag initially contains 1 red and 2 blue balls. An experiment consisting of selecting a ball at random, noting its color and replacing it together with an additional ball of the same color. If three such trials are made, then (a)Probability that a t least one blue ball is drawn is 0.9 (b)Probability that exactly one blue ball is drawn is 0.2 (c)Probability that all the drawn balls are red given that all the drawn balls are of same color is 0.2 (d)Probability that at least one red bal is drawn is 0.6

A bag contains four one-rupee coins, two twenty-five paisa coins, and five ten-paisa coins. In how many ways can an amount, not less than Rs. 1 be taken out from the bag? (Consider coins of the same denominations to be identical.) a. 71 b. 72 c. 73 d. 80