Question

in how many ways can the letters of the word 'LANGUAGE' be arranged in such a way that the vowel always com together

Answer 1

Answer:

720

Step-by-step explanation:

The word is = LANGUAGE

Vowels = AUAE

consonants= LNGG

Lets take all the vowels as a single unit and all consonents different unit

Total no of ways = (5!/2!) * (4!/2!)

= 60* 12

720

I hope this will help you

Answer 2

Answer:

The number of words can be formed is 720 words  

Step-by-step explanation:  

Given word  LANGUAGE  

⇒ here we need to calculate number of words can be arranged in a such a way that all vowels always come together

⇒ Vowel letters in given word = A U A E

⇒ Consonants in given word = L N G G  

⇒ now take A U A E  as 1 unit

⇒ number of words can be formed with  (AUAE ) and L N G G = 5!/2!

⇒ The number of words can be formed with A U A E = 4!/ 2!

⇒ the number words can be formed in a way that the vowels come together =  $\frac{5!}{2!}$ × $\frac{4!}{2!}$  =  $\frac{5(4)(3)(2!)}{2!}$ $\frac{4(3)(2!)}{2!}$  = 5×4×3×4×3 = 720

⇒ The number of words can be formed = 720 words