Question

Find the number of arrangements of the letters of the word REPUBLIC. How many arrangements start with a vowel ?

Answer 1

Answer:

The number of arrangements of the letters of the word REPUBLIC is 40320.

Total arrangements start with a vowel is 30240.

Step-by-step explanation:

Given : Letters of word REPUBLIC

To find : The number of arrangements of the letters of the word REPUBLIC?

How many arrangements start with a vowel ?

Solution :

Total number of words in the word REPUBLIC = 8

Total number of arrangement's = 8!

$8!=8\times 7\times 6\times 5\times 4\times 3 \times 2\times 1$

$8!=40320$

The number of arrangements of the letters of the word REPUBLIC is 40320.

Number of vowels in the word REPUBLIC is 3 (E,U,I)

Word start with a vowel so first space is filled with vowels

Ways of first place is 3!

Rest seven places have 7!

Total arrangements = $3!\times 7!$

Total arrangements = $30240$

Total arrangements start with a vowel is 30240.