Abstracted secretary placed three letters randomly into three envelopes. what is the probability that at least one of the recipients gets his letter ?

The probability is 0.6666

Step-by-step explanation:

First, the total number of ways in which the secretary could place the three letters into three envelopes is calculated using the rule of multiplication as:

    3                *         2               *              1                =     6

1st envelope      2nd envelope     3rd envelope

Because, we have 3 letters for the 1st envelope, then 2 letters for the 2nd envelope and finally 1 letter for the 3rd envelope.

Then, if at least one of the recipients get his letter, it means that:

So, we have 4 ways in which at least one of the recipients gets his letter.

Finally, the probability can be calculate as:

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)