How many ways can the letters of the word MAKABANSA be arranged in a row? A.15 1...

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October 2022 1 4 Report

How many ways can the letters of the word MAKABANSA be arranged in a row?
A.15 120
B.90 720
C.362 880

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$\underline{\mathbb{QUESTION:}}$

- How many ways can the letters of the word MAKABANSA be arranged in a row?

A. 15,120
B. 90,720
C. 362,880

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

$\qquad\LARGE\rm» \:\: \green{A. \: 15\text,120}$

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

- This 9-letter words can be arranged in 9! ways and remove the other repeating arrangements such that 4 A's is arranged in 4! ways.

$\begin{aligned} &\bold{\color{lightblue}Formula:} \\ & \boxed{\: \rm P = \frac{n!}{n_1! \ n_2! \ ... \ n_k!} \:} \end{aligned}$

$\begin{aligned} \rm P = \frac{9!}{4!} \end{aligned}$

$\begin{aligned} \rm P = \frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot \cancel{4!}}{ \cancel{4!}} \end{aligned}$

$\rm P = 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5$

$\rm P = 15\text,120$

$\therefore$ There are 15,120 ways to arrange the letters of the word MAKABANSA.

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