Question

How many words with or without meaning,each of 3 vowels & 2 consonants can be formed from the letters of the word EQUATION?

Answer 1

number of vowels=5

number of consonant =3

number of vowels can be arranged =5p5

=5/(5-5)

=5/0=5/1=120

number of consonant can be arranged =3p3

=3/(3-3)

=3/0=3/1=6

Answer 2

Answer:

Number of words = 3600

Step-by-step explanation:

Given:

• The word EQUATION

To Find:

• How many words with or without meaning can be formed from the letters of the given word each of 3 vowels and 2 consonants

Solution:

First finding the total number of consonants and vowels in the given word.

Number of vowels = 5 (E, U, A, I, O)

Number of consonants = 3 (Q, T, N)

Hence,

Total number of ways the 2 consonants and 3 vowels can be selected is given by,

$\sf Total\:number\:of\:ways= \:^{5} C_3\times \: ^{3} C_2$

We know that,

$\boxed{\sf ^{n} C_r=\dfrac{n!}{r!(n-r)!} }$

Hence,

$\sf Total\:number\:of\:ways=\dfrac{5!}{3!(5-3)!} \times \dfrac{3!}{2!(3-2)!}$

$\sf \implies \dfrac{5!}{3!\times 2!} \times \dfrac{3!}{2!\times 1!}$

$\sf \implies \dfrac{5\times4\times 3!}{3!\times 2!} \times \dfrac{3\times 2!}{2!\times 1!}$

$\sf \implies \dfrac{5\times4}{ 2} \times 3$

$\sf \implies 30$

Hence the total number of ways 3 vowels and 2 consonants can be selected is 30.

Now finding the number of ways of arranging the 5 letters,

Number of arrangements  = 5!

Number of words that can be formed by 3 vowels and 2 consonants = Total number of arrangements of letters × Number of ways the letters can be selected.

Substitute the data,

Total number of words formed = 5! × 30

⇒ 5 × 4 × 3 × 2 × 30

⇒ 3600

Hence 3600 words can be formed each of 3 vowels and 2 consonants.