Distinct signals flag problem

Question

How many distinct signals can be made using four flags in a row, if there are available just three red, one white, and two black flags?

Answer 1

3 red flags

------------------------

2* (4 choose (3,1)) <--- 3 red and 1 of either red or black

= 8

rrrw rrrb

rrwr rrbr

rwrr rbrr

wrrr brrr

2 red flags

-------------

(4 choose (2,1,1) )=12 <---- 1 black and 1 white

(4 choose (2,2) ) =6<--- 2 red and 2 black

rrbw rbrw brrw

rrwb rbwr brwr

rwrb rwbr bwrr

wrrb wrbr wbrr

rrbb bbrr

rbrb brbr

brrb rbbr

1 red flag

------------

( 4 choose (1,2,1))=12 <--- 1 red, 2 black, 1 white

rbbw bbrw wbrb

rbwb bbwr wbbr

rwbb bwbr brbw

wrbb bwrb rbbw

38