A delegation of 4 students is to be selected from 12 students; find number of ways of doing so if; a) two students wish to be included together only in the delegation b) if two particular students refuse to be together and two other students wish to be together in delegation only
Well first off, i thought the wording was really weird. I don't understand what 'in delegation' means. Looking at answer, i assumed it is
in case a) that either both are selected or both not selected and
in case b) two students don't want to be together and the other two want to be together irrespective of whether they are both in or out
So my first question is, Is this what the question is actually asking?
My solutions;
a) if both are selected ${10\choose2}$ and if both are not selected, then ${10\choose4}$. So total = 45 + 210 = 255.
b) Let $H_1 , H_2$ be kids who don't want to be together and $L_1 , L_2 $ be kids who want to be together. So, only one of $H_1 / H_2$ will be selected.
case 1) $L_1, L_2$ not selected => ${8\choose4} \cdot 2$
case 2) $L_1,L_2$ selected => ${8\choose2} \cdot 2$
So total = 196. But actual answer is 226
I don't understand where I am wrong, any help is appreciated.