Q1 of 43 Page 296

If the letters of the word ALGORITHM are arranged at random in a row what is the probability the letters GOR must remain together as a unit?

Given word is ALGORITHM

⇒ Total number of letters in algorithm = 9


∴ Total number of words = 9!


So, n(S) = 9!


If ‘GOR’ remain together, then we consider it as one group.



∴ Number of letters = 7


Number of words, if ‘GOR’ remain together in the order = 7!


So, n(E) = 7!




[∵ n! = n×(n – 1)×(n – 2)…1]



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2

Six new employees, two of whom are married to each other, are to be assigned six desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have nonadjacent desks?

 3

Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.

 4

An experiment consists of rolling a die until a 2 appears.

(i) How many elements of the sample space correspond to the event that the 2 appears on the kth roll of the die?


(ii) How many elements of the sample space correspond to the event that the 2 appears not later than the kth roll of the die?

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A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.