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GarryVolchara [31]

3 years ago

5

How many distinguishable 7 letter "words" can be formed using the letters in alabamaalabama?

1 answer:

otez555 [7]3 years ago

3 0

<span>You are given the word alabama and you are asked to find how many distinguishable 7 letter "words" can be formed from it.

ALABAMA has seven letters so we will start at 7!
Counting the number of A's in the word we have 4 A's and so we will divide it by 4!
</span>Counting the number of L's in the word we have 1 L and so we will divide it by 1!
Counting the number of B's in the word we have 1 B and so we will divide it by 1!
Counting the number of M's in the word we have 1 M and so we will divide it by 1!

And so the number of ways is 7! / (4! x 1! x 1! x 1!) = 210 words.

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How to differentiate y=x^n using the first principle. In this question, I cannot use the rule of differentiation. I have to do t

Zarrin [17]

By first principles, the derivative is

$\displaystyle\lim_{h\to0}\frac{(x+h)^n-x^n}h$

Use the binomial theorem to expand the numerator:

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where

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The first term is eliminated, and the limit is

$\displaystyle\lim_{h\to0}\frac{nx^{n-1}h+\dfrac{n(n-1)}2x^{n-2}h^2+\cdots+nxh^{n-1}+h^n}h$

A power of $h$ in every term of the numerator cancels with $h$ in the denominator:

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Finally, each term containing $h$ approaches 0 as $h\to0$ , and the derivative is

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3 years ago

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olganol [36]

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