Individual A has a circle of five close friends (B, C, D, E, and F). A has heard a certain rumor from outside the circle and has invited the five friends to a party to circulate the rumor. To begin, A selects one of the five at random and tells the rumor to the chosen individual. That individual then selects at random one of the four remaining individuals and repeats the rumor. Continuing, a new individual is selected from those not already having heard the rumor by the individual who has just heard it, until everyone has been told. a. What is the probability that the rumor is repeated in the order B, C, D, E, and F?
b. What is the probability that F is the third person at the party to be told the rumor?
c. What is the probability that F is the last person to hear the rumor?
d. If at each stage the person who currently "has" the rumor does not know who has already heard it and selects the next recipient at random from all five possible individuals, what is the probability that F has still not heard the rumor after it has been told ten times at the party?

Step-by-step explanation:

From the given information;

The possible number of ways to select these people in order B, C, D, E, and F is:

= 5 × 4 × 3 × 2 × 1

= 120

However, using the order B, C, D, E, and F; The probability that the rumor is repeated is:

= 1/120

= 0.0083

b)

If we make F the subject here by selecting it such that F has not been selected in the first and second draw;

Then:

The possible numbers of ways to select F as third = 4 × 3 × 2 × 1

= 24

Now;

the required probability of F is the third person: = 24/120

= 0.2

c)

Suppose F is selected as the last person to hear the rumor;

Then, the selection of F in the last row = 4 × 3 × 2 × 1

Recall that; the total possible number of ways to select the person is B, C, D,E, and F which is = 120

Then, the required probability of F as the last person to hear the rumor is:

= 24/120

= 0.2

d)

Here, the required probability of F since F has not heard the rumor after it has been told tren times is:

= 4¹⁰

Let's no forget that the total number of possible ways to select the persons using the above criteria is = 5¹⁰

Thus, the required probability of F = 4¹⁰/5¹⁰

= 0.1074

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