Question

In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

Answer 1

(3! + 2! + 1!) * 2

Answer 2

for AAU, and consonants B, C, and S

AAUBCS
AAUCBS
AAUBSC
AAUCSB
AAUSBC
AAUSCB

CSBAAU
BSCAAU
CBSAAU
BCSAAU
SBCAAU
SCBAAU

CAAUSB
SAAUBC
BAAUSC
BAAUCS
CAAUBS
SAAUCB

CSAAUB
SBAAUC
BSAAUC
BCAAUS
CBAAUS
SCAAUB

Answer 3

now multiply 24 by the number of ways we can arrange AAU

Answer 4

AAU, AUA, UUA. so it is 24 * 3 = 72

Answer 5

Yeah, I went dumb on this one, lol