Find the number of selections that can be made taking 4 letters from the word "ENTRANCE". Options
A) 70  B) 36  C) 35  D) 72  E) 32
We have 8 letters from which 6 are unique.   Possible scenarios for 4 letter selection are:   A. All letters are different;   B. 2 N-s and other letters are different;   C. 2 E-s and other letters are different;   D. 2 N-s, 2 E-s.   Let's count them separately:   A. All letters are different, means that basically we are choosing 4 letters form 6 distinct letters: 6C4=15;   B. 2 N-s and other letters are different: 2C2(2 N-s out of 2)*5C2(other 2 letters from distinct 5 letters left)=10;   C. 2 E-s and other letters are different: 2C2(2 E-s out of 2)*5C2(other 2 letters from distinct 5 letters left)=10;;   D. 2 N-s, 2 E-s: 2C2*2C2=1.   15+10+10+1= 
<gadget id="calculator">15+10+10+1</gadget>
<output>36</output>
36   Answer: 36.
<result>B</result>
Find the number of selections that can be made taking 4 letters from the word "ENTRANCE".