Messages are conveyed by arranging four white, one blue, and three red flags on a pole. Flags of the same color are alike. If a message is transmitted by the order in which the colors are arranged, the total number of messages that can be transmitted if exactly six flags are used is a. `45` b. `65` c. `125` d. `185`

There are 2 identical white balls, 3 identical red balls, and 4 green balls of different shades. Find the number of ways in which they can be arranged in a row so that at least one ball is separated from the balls of the same color.

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 library has a copies of one book, b copies each of two books, c copies each of three books, a single copy of d books. The total number of ways in which these books can be arranged in a shelf is equal to a. ((a+2b+3c+d)!)/(a !(b !)^2(c !)^3) b. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^3) c. ((a+b+3c+d)!)/((c !)^3) d. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^)