Solveeit Logo
Login

Question

Question: If in a group of five married couples each male shakes hand with exactly one female similarly each f...

If in a group of five married couples each male shakes hand with exactly one female similarly each female shakes hand with exactly one male, then the probability that no husband shake hands with his own wife, is

A

2324\frac{23}{24}

B

1125\frac{11}{25}

C

119120\frac{119}{120}

D

1130\frac{11}{30}

Answer

1130\frac{11}{30}

Explanation

Solution

dearrangementof5objects5!=44120=1130\frac{\mathbf{dearrangementof5objects}}{\mathbf{5!}}\mathbf{=}\frac{\mathbf{44}}{\mathbf{120}}\mathbf{=}\frac{\mathbf{11}}{\mathbf{30}}