Question

In how many ways the letter of the word 'references' can be arranged so that vowels remains together

Answer 1

Answer:

Total arrangemnets = 20160

Step-by-step explanation:

Given the word

REFERENCES

Total number of words in the letter = 10

Vowels in the words are E, E, E

No. of vowels = 3

No. of consonents = 10 - 3 = 7

If we make a bundle of all the vowels, they can be arranged only in one way because they all are same

Therefore, taking vowel as a single entity and the remaining 7 letters we get in total 8 objects to be arranged. Since the word contains two R s, out of these 8 objects 2 are same

Therefore total arrangements

$=\frac{8!}{2!}$

$=4\times7!$

$=20160$