Question

How many words can be formed using all the let ters of the word SPECTRA so that all the vowels are always together?

• A. 720
• B. 360
• C. 1440
• D. 180

Answer 1

The correct option is C 1440

The word 'SPECTRA' has $7$ letters. It has the vowels E, A, in it and these $2$ vowels should always come together. Hence these $2$ vowels can be grouped and considered as a single letter. That is, we have finally $6$ letters S,P,C,T,R, (EA)
As all these $6$ letters are different,
Number of ways to arrange these letters to form words ${=}^6{P}_6=\frac{6!}{(6-6)!}=\frac{6!}{0!}=6!=6\times 5\times 4\times 3\times 2\times 1=720$
Also, both the $2$ vowels (EA) are different
Number of ways to arrange these vowels among themselves = $2!=2\times 1=2$
Hence, required number of ways $720\times 2=1440$ ways