[Math] how to arrange vowels be arranged in even places given the following conditions

combinatoricspermutations

In how many ways can the letters of the word RESULT be arranged so that the vowels appear in even places only?

options:

a) $0$ b) $48$ c) $120$ d) $144$

MyApproach:

RESULT has $2$ vowels and $4$ consonants.

$2$ vowels can be arranged in $3$ places in $3C2$ ways and the rest can be arranged in $4!$ ways.

Therefore $4!$ . $3C2$=$72$

Can Anyone give me the hint if I am wrong?

Best Answer

You took order into account for the consonants but not for the vowels. That's the missing factor $2$.