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klasskru [66]
1 year ago
13

A password is 4 characters long and must consist of 3 letters and 1 of 10 special characters. If letters can be repeated and the

special character is at the end of the password, how many possibilities are there? a. 175,760 b. 456,976 c. 703,040 d. 1,679,616 Please select the best answer from the choices provided A B C D.
Mathematics
1 answer:
Ne4ueva [31]1 year ago
5 0

The number of possibilities for constructing the 4 characters long password with specified conditions is given by: Option C: 703,040

<h3>What is the rule of product in combinatorics?</h3>

If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in p \times q ways.

Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.

Thus, doing A then B is considered same as doing B then A

We're specified that:

  • The password needs to be 4 characters long
  • It must have 3 letters and 1 of 10 special characters.
  • Repetition is allowed.

So, each of 3 characters get 26 ways of being 1 letter. (assuming no difference is there between upper case letter and lower case letter).

And that 1 remaining character get 10 ways of being a special character.

So, by product rule, this choice (without ordering) can be done in:

26 \times 26 \times 26 \times 10 = 175760 ways.

Now, the password may look like one of those:

  1. L, L, L, S
  2. L, L, S, L
  3. L, S, L, L
  4. S, L, L, L

where S shows presence of special character and L shows presence of letter.

Those 175760 ways are available for each of those four ways.

Thus, resultant number of ways this can be done is:

175760 \times 4 = 703040

Thus, the number of possibilities for constructing the 4 characters long password with specified conditions is given by: Option C: 703,040

Learn more about rule of product here:

brainly.com/question/2763785

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Rewrite Linear equation in slope intercept form: 12x-3y=18
shutvik [7]

Answer:

y = 4x - 6

Step-by-step explanation:

12x - 3y = 18 is in standard form. We need to convert it to slope-intercept form, which looks like y = mx + b, with m being the slope and b being the y-intercept.

We know that 12x has to do with our slope, and 18 is our y-intercept. We need to put those on the right side of the equation so that we can isolate y on the left side:

12x - 3y = 18

Subtract 12x from both sides.

-3y = -12x + 18

Now, we can divide both sides by -3 to get y by itself.

y = 4x - 6

And that looks like slope-intercept form (y = mx + b).

Hopefully this was helpful! If you have more questions, let me know. :)

7 0
2 years ago
Please help.................. really need to get this right
Marina CMI [18]
the correct answer is none of the above
6 0
3 years ago
Ellen is playing a video game in which she captures butterflies. There are 5 butterflies onscreen, but the number of butterflies
vovikov84 [41]
(Each minute+1)((Number of butterflies)^2)
5 0
3 years ago
Q4.
Levart [38]

Probabilities are used to determine the chances of an event

  • The probability of choosing a black counter is 0.6
  • The probability that both counters are white is 0.16

<h3>(a) Probability of selecting two blacks</h3>

The probability is given as:

P(Black\ n\ Black)=0.36

Apply probability formula

P(Black) \times P(Black)=0.36

Express as squares

P(Black)^2=0.36

Take the square root of both sides

P(Black)=0.6

Hence, the probability of choosing a black counter is 0.6

<h3>(b) Probability of selecting two white counters</h3>

In (a), we have:

P(Black)=0.6

Using the complement rule, we have:

P(White) = 1 - P(Black)

So, we have:

P(White) = 1 -0.6

Evaluate

P(White) = 0.4

The probability that both counters are white is then calculated as:

P(White\ and\ White) = P(White) \times P(White)

So, we have:

P(White\ and\ White) =0.4 \times 0.4

P(White\ and\ White) =0.16

Hence, the probability that both counters are white is 0.16

Read more about probabilities at:

brainly.com/question/15858152

6 0
2 years ago
3x−1=1−3x. Needs to be in simpilest form.
xz_007 [3.2K]

Answer:

x= 2/6

Step-by-step explanation:

add 3x to both sides

add 1 to both sides

divide 6 to both sides to isolate x

x = 2/6

8 0
3 years ago
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