In how many different ways can the letters of the word 'APTITUTE' be arranged so that all the vowels are in the beginning? [closed]

In how many different ways the letters of the word 'APTITUTE' can be arranged so that all the vowels always in beginning ?

1. $48$
2. $72$
3. $576$
4. $2880$
5. $960$

closed as off-topic by Dylan, Misha Lavrov, Rolf Hoyer, user99914, JMPNov 14 '17 at 5:10

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1 Answer

Vowels $A,I,U,E$.

Consonants $P,T,T,T$.

We start with 4 vowels, all distinct, this gives us $4! = 24$ ways. We then order the consonants, which have $\frac{4!}{3!} = 4$ ways. (there are 4 places for the $P$, essentially).

So in total I get $24 \times 4 = 96$ ways, which is not mentioned among your alternatives. Question for OP: did I interpret the question in a wrong way?

• i guess the options are wrong.....i thought the same way – drek Jul 16 '17 at 8:07