Difference between revisions of "2015 AMC 10A Problems/Problem 10"
Happycowzh (talk | contribs) (Created page with "==Solution== Observe that we can't begin a rearrangement with either a or d, leaving bcd and abc, respectively. Starting with b, there is only one rearrangement: <math>bdac</ma...") |
Happycowzh (talk | contribs) (→Solution) |
||
| Line 1: | Line 1: | ||
| + | ==Problem== | ||
| + | |||
| + | How many rearrangements of <math>abcd</math> are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either <math>ab</math> or <math>ba</math>. | ||
| + | |||
| + | <math> \textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}}\ 3\qquad\textbf{(E)}\ 4</math> | ||
| + | |||
| + | |||
==Solution== | ==Solution== | ||
Revision as of 14:25, 4 February 2015
Problem
How many rearrangements of 
are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either 
or 
.
$\textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}}\ 3\qquad\textbf{(E)}\ 4$ (Error compiling LaTeX. Unknown error_msg)
Solution
Observe that we can't begin a rearrangement with either a or d, leaving bcd and abc, respectively.
Starting with b, there is only one rearrangement: 
. Similarly, there is only one rearrangement when we start with c: 
.
Therefore, our answer must be 
.
