<p>If only 4-letter patterns can be formed from the following units and no letter occurs more than once, then how many of these patterns begin with a vowel and end with a consonant:
a,e,i,o,r,s,and t? </p>
<p>I know we can solve this using the counting principle, but I cannot get the order right.
Please help! Thanks.</p>
<p>It is always easiest to do the special cases first. In this case that’s the first and last letter. There are 4 choices for the first letter (4 vowels), and 3 choices for the last letter (3 consonants). After that we have 5 and 4 choices for the remaining 2 positions. So the answer is:</p>
<p>4<em>3</em>5*4 = 240.</p>
<p>DrSteve, you sir are beyond laudation. Thank you a million times.</p>