Asked Apr 4, 2019

The following problems refer to strings in A to Z. 

(a) how many diffrent four letter strings are there? 

(b) How many four letter stings are there that begin with X? 

(C) How many four- letter stings are there that contain exactly two x's? 


Expert Answer

Step 1

In this question, we have to form a four letter strings using the letters A to Z.

Since in this question it has not mentioned that repetition is allowed or not, that’s why we are considering that repetition is allowed.

There are 26 letters from A to Z,

Step 2

Part a.) how many different four-letter strings are there?


We have to form a four-letter string, and we have 26 letters

To fill the 1st place we have 26 options

To fill the 2nd place we have 26 options

To fill the 3rd place we have 26 options

And for the last and 4th place we have 26 options

Calculations shown on the whiteboard.

Step 3

(b) How many four-letter stings are there that begin with X? 


Now, we have to form a 4-letter string which begins with letter X

Which means now, the 1st place has already been allotted by X means equal to 1.

Now, to fill the 2nd place we have 26 options

To fill the 3rd place we have 25 options

And for the last and 4th place now we have 26 ...


Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in



Related Probability Q&A

Find answers to questions asked by student like you
Show more Q&A

Q: A die is rolled six times.  What is the probability of obtaining two 5's?

A: Introduction to binomial distribution:Consider a random experiment involving n independent trials, s...


Q: In a​ five-card poker​ hand, what is the probability of being dealt exactly one six and no picture c...

A: For any event A and the sample space S, the probability can be found as,


Q: In a student body, 50% use Google Chrome, 12% use Internet Explorer, 10% Firefox, 5% Mozilla, and th...

A: Click to see the answer


Q: You draw one card from a​ 52-card deck. Then the card is replaced in the deck and the deck is shuffl...

A: The total number of cards in deck = 52The total number of jacks in deck of cards = 4the probability ...


Q: Need help on this concept

A: Hello. The information about the nine sheets of paper is missing in the question and hence we are no...


Q: A single, six-sided die is rolled. Find the probability of rolling an even number or a number less t...

A: Addition rule of probability:Addition rule of probability indicates the happening either of the even...


Q: Motors Inc. manufactured 325 cars with automatic transmissions, 216 with power steering, and 89with ...

A: Consider the provided information:Number of cars manufactured with automatic transmissions, n(A) = 3...


Q: Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the wat...

A: In this question, the average lifetime of Quartz crystal Watches follows normal distribution with me...


Q: One option in a roulette game is to bet $13 on red.​ (There are 18 red compartments, 18 black ​compa...

A: The total number of red compartments = 18The total number of non red compartments  = 18=2 = 20The to...