Question

in how many ways can the letter of the words RECTANGLE be arranged,such that all the vowels are always together ​

Answer 1

Given :   word "RECTANGLE"  

all the vowels are always together ​

To find :  Number of ways

Solution:

RECTANGLE

has  9 letters

Vowels   E A  E    =  3  and E is repeated

Consonants  R C  T  N  G  L      

Make a group of vowels so that they always together

vowel with in group can be arranged in 3!/2!  =  3 Ways

Now 1 group of vowel + 6 consonants  

Hence total = 7

& can be arranged in 7!  ways

Total Ways  =  3 * 7!

= 15120

in 15120 ways  the letter of the words RECTANGLE can be arranged ,such that all the vowels are always together

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