An absent-minded secretary prepares an envelope for each of five letters to different people. He then randomly puts the letters into the envelopes. Find the probability function for the number of letters that are placed in the correct envelope.

5C1/5!

Step-by-step explanation:

there are 5! Ways of arranging the envelope .

Then to get the probability that it is selected to match 5 letters with accuracy (5C1) is actually 5C1/5.

This law is from combination law with respect to the above probability question, as combination deals with selection, and helps in probability.

Probability = Number of correct ways/ Number of total ways

Probability = 1/120

Probability = 0.0083

Step-by-step explanation:

Let L represents letters and E represents envelops

There are total 5 letters and 5 envelopes.

There is only one correct order of placing each letter into corresponding envelope.

L1 -> E1, L2 -> E2, L3 -> E3, L4 -> E4, L5 -> E5

What is the total number of ways this can be done?

Total number of ways = 5*4*3*2*1 = 120

So the probability function is

Probability = Number of correct ways/ Number of total ways

Probability = 1/120

Probability = 0.0083

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2