how many groups can be made from the word "house" if each group consists of 4 alphabets?with solution . Created by help7386. Math

how many groups can be made from the word "house" if each group consists of 4 al...

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$\large\underline{\mathbb{ANSWER}:}$

$\qquad \LARGE \:\: \rm 5 \: Groups$

*Please read and understand my solution. Don't just rely on my direct answer*

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$\large\underline{\mathbb{SOLUTION}:}$

Since the letters are grouped, the order doesn't matter. Solve for the number of combinations does 5 letters picked 4 at a time.

$\begin{align} & \bold{Formula:} \\ & \quad \boxed{\rm _nC_r = \frac{n!}{r!(n-r)!}} \end{align}$

$\rm _5C_4 = \frac{5!}{4!(5-4)!} \\$

$\rm _5C_4 = \frac{5!}{4! \,1!} \\$

$\rm _5C_4 = \frac{5 \cdot \cancel{4!}}{\cancel{4!} } \\$

$\rm _5C_4 = 5$

Therefore, there are 5 groups of 4 letters that can be made from the word "house".

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PROBLEM:

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How many groups can be made from the word "house" if each group consists of 4 alphabets?

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SOLUTION:

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Number of letters in the word (house) = 5

Number of alphabets in each group = 4

Therefore, number of such groups

$\: • \: \: \sf{5c _4}$

$\: • \: \: \boxed{\sf{5}}$

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ANSWER:

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Therefore, the 5 groups can be made from the word "house" if each group consists of 4 alphabets.

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