Question

in how many ways the word ORANGE can be arranged so vowels are together​

Answer 1

Answer:

144

First lets organize out 4 possibilities of vowels (V) vs consonants (C)

VCVCVC, VCVCCV, VCCVCV, CVCVCV

Now within those 4 combinations there are 6 ways to order the 3 consonants

RNG, RGN, GRN, GNR, NRG, NGR

And likewise 6 ways to order the 3 vowels

OAE, OEA, EAO, EOA, AEO, AOE

So in total there are 6*6*4=144 different ways to arrange the letters of ORANGE so that none of the vowels are next to eachother.