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, JMP Nov 14 '17 at 5:10

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  • $\begingroup$ Welcome to MathSE. When you pose a question here, it is expected that you state the context in which you encountered the problem and your own thoughts on the problem. For an exercise such as this, you should state what you have tried and where you are stuck so that you receive responses appropriate to your skill level. $\endgroup$ – N. F. Taussig Jul 16 '17 at 7:36

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?

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

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