<p>I came across this math questions that i apparently can't get my head around ...</p>
<p>Two vowels, a and e, and two consonants, m and t, are to be arranged to form a four-letter code. How many of these codes are possible if the vowels and consonants must alternate ?</p>
<p>A. 6
B. 8
C.12
D. 16
E. 24</p>
<p>Answer is B, but i did it non-mathematically. I just wrote out the possible combinations:</p>
<p>mate
meta
tame
tema
amet
atem
emat
etam</p>
<p>Took like a minute, which may be more than one might want to spend on a questions like this.</p>
<p>Good question.</p>
<p>For this type of question, think of how many possibilities there are for each position, and then multiply them.</p>
<p>First position: 4 possibilities.
(Any of the 4 letters can go there at the start.)
Second position: 2 possibilities.
(If the first position was filled with a vowel, there are 2 consonants to choose from, and vice versa.)
Third position: 1 possibility.
(Must be the remaining vowel or consonant consonant, whichever was chosen first.)
Fourth position: 1 possibility.</p>
<p>4x2x1x1 = 8</p>
<p>Ohh, i got it <em>High five</em>
Thanks for the help ;)</p>