# 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?

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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?

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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?

Solution:

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 ...

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