Answered

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How many 5-letter words can be made using exactly 5 of the letters from
TEXAS and MEXICO? Letters may only be used as many times as they appear. (For
example, XETEX is allowed. However, MATEA is not allowed, since the A appears twice
in MATEA but only once in the given words.)

Sagot :

The total number of ways by words are formed is 35 ways.

According to the statement

We have given that the 5 letters and we have to make word from them and the letters are repeated as equal to letters in given words.

And we have to find the possible ways.

So, The given words are:

TEXAS and MEXICO

Here X = 2 and E = 2 and all other words are one time used words.

We can find possible ways by use of combination and permutation.

So,

Total number of ways = [tex]3C_{1} ^{5} + 2C_{2} ^{5}[/tex]

here 3 because three letters are not repeatable and 2 letters are repeated for 2 times.

So,

Total number of ways = [tex]3C_{1} ^{5} + 2C_{2} ^{5}[/tex]

Total number of ways = [tex]3(\frac{5!}{1!} ) + 2(\frac{5!}{2!*3!} )[/tex]

Total number of ways = [tex]3(5) + 2(10)[/tex]

Total number of ways = 15 + 20

Total number of ways = 35.

So, The total number of ways by letters are formed is 35 ways.

Learn more about combination and permutation here

https://brainly.com/question/11732255

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