Kumar has ten friends among whom two are married to each other. He wishes to invite five of them for a party. If the married refuse to attend separately, then the no. of different ways in which he can invite five friends is

No.of ways of inviting

i) married couple and 3 other=$=\left({ }^2{C}_2{\times }^8{C}_3\right)$

ii) 5 others (excluding married couple) $=\left({ }^2{C}_0{\times }^8{C}_5\right)$

Total no.of ways=$=\left({ }^8{C}_3{+}^8{C}_5\right)=2{\times }^8{C}_{3}OR$

Required= (Total combinations of 5 persons)-(Combinations containing)

Only one out of married couple  ${=}^{10}{C}_5-\left({ }^2{C}_1{\times }^8{C}_4\right)$