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

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${2.}^{8} C_{3}$

$^{10} C_{5} - {2.}^{8} C_{4}$

$^{8} C_{5}$

$^{10} C_{5}$

answer is B, C.

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Detailed Solution

No.of ways of inviting

i) married couple and 3 other= $= (^{2} C_{2} \times^{8} C_{3})$

ii) 5 others (excluding married couple) $= (^{2} C_{0} \times^{8} C_{5})$

Total no.of ways= $= (^{8} C_{3} +^{8} C_{5}) = 2 \times^{8} C_{3} O R$

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

Only one out of married couple $=^{10} C_{5} - (^{2} C_{1} \times^{8} C_{4})$

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