How many different 4-digit numbers can be written using the digits 1 to 8 without repetition such that the number always contains the digit 2? Answers:
A) 360
B) 560
C) 760
D) 840
E) 1260
The most restrictive case. We should have a two.   No repetition. Numbers range from 1 to 8.   = 1*7*6*5= 
<gadget id="calculator">1*7*6*5</gadget>
<output>210</output>
210 ways we can write if '2' is in the first position.= 4*(210)= 
<gadget id="calculator">4*(210)</gadget>
<output>840</output>
840 ways.   Another method.   Without restriction for 8 digits- 8*7*6*5= 1680 Ways we can write.   Without restriction for 7 digits- 7*6*5*4 = 840 Ways.   With restriction = 1680 - 840= 
<gadget id="calculator">1680 - 840</gadget>
<output>840</output>
840 Ways.   ANSWER:840
<result>D</result>
How many different 4-digit numbers can be written using the digits 1 to 8 without repetition such that the number always contains the digit 2?