In how many ways can a five-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password? Answers
A) 420 B) 576 C) 900 D) 936 E) 1,296
Total number of four letter passwords = 6*6*6*6= 
<gadget id="calculator">6*6*6*6</gadget>
<output>1_296</output>
1296 ------(1)   Total number of passwords in which no letter repeats= 6C5*5!= 6*120= 
<gadget id="calculator">6*120</gadget>
<output>720</output>
720------(2)   therefore required value= (1)-(2)= 1296-720= 
<gadget id="calculator">1296-720</gadget>
<output>576</output>
576   576
<result>B</result>
In how many ways can a five-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?