The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly five elements each?
Choices.
A) 120	B) 126	C) 130	D) 140	E) 144
nC2 = 36   =&gt; n*(n-1)/2 = 36 by middle term factor and n cannot be -ve   =&gt; n = 9   nC3 = 9C5 = 9!/5!(9-5)!= 9*8*7*6*5!/5!*4*3*2*1= 126   So, Answer is 126   .
<result>B</result>
The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly five elements each?