In how many different ways can the letters of the word "TRANSPORT" be arranged the vowels always come together?
Solution
In the word TRANSPORT, AO are the only vowels and remaining letters are TTRRNSP.
We will make 1 bundle of AO and will have 1 + 7 = 8 letters to arrange with 2Ts and 2Rs.
They can be arranged in $$\frac{8!}{2!\times\ 2!}$$ ways and the letters of the bundle can also be arranged in 2! ways which gives a total of $$\frac{8!}{2!\times\ 2!}\times\ 2!=\frac{8!}{2!}=20160$$.
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