What is the value of (14!/(12!·2!) − 13!/(11!·2!))?

Correct answer: 13

The governing method is factorial cancellation followed by subtraction. For the first term, 14!/(12!·2!)=(14×13)/(2×1)=182/2=91. For the second term, 13!/(11!·2!)=(13×12)/(2×1)=156/2=78. The required expression is therefore 91−78=13, so option A is correct. Another efficient check is to recognize the two terms as 14C2 and 13C2, whose difference is 91−78. Option B would come from adding equal-looking differences rather than evaluating the stated subtraction. Options C and D result from incorrect combinations of the intermediate products. The 2! denominator must be retained in both terms before subtraction.