A, B,C, D,E, F,are to give speeches to the class . The order of speeches is determined by randomly selection. Compute the probability that E will speak first and Cwill speak fifth

1/30

Explanation:

To solve this we lay out the order of speeches and the number of people to fill in that position. We first find the number of desirable outcomes

Conditions:

- E speaks first

- C speaks fifth

In the first position, there is only one option which is E.

In the second position, we can choose from 4 others (E is in first, and C is reserved for fifth)

In the third, we can choose from 3 others (4 - 1)

In the fourth, 2 choices (3 - 1)

In the fifth, there is only one choice as it needs to be speaker C.

In the sixth is the remaining person from the 2 choices for fourth position (2 - 1)

Now we multiply to get the number of desirable outcomes

1x4x3x2x1x1 = 24

After that, we get the total number of outcomes. To find the probability, we divide the number of desirable outcomes by the total number of outcomes.

The total number of outcomes is 6! = 720

So:

24/720 = 1/30 simplified