Question

The number of ways in which a mixed doubles game in tennis can be arranged from $5$ married couples, if no husband and wife play in the same game, is

• A. $46$
• B. $54$
• C. $60$
• D. None of these

Answer 1

The correct option is C

$60$

The explanation for the correct answer.

Find the number of ways:

Given: There are $5$ married couples.

Since no husband and wife can play together.

Let the sides of the game be $A$ and $B$.

$2$ husbands for two sides $A$ and $B$ can be selected out of $5={}^5{\mathrm{C}}_2=10$ ways.

Now we have two excluded their wives.

So we have to choose $2$ wives out of the remaining $3$ wives' $={}^3{\mathrm{C}}_2=3$ ways.

Two wives can interchange their sides in $2!=2$ ways.

Therefore the total number of ways$=10\times 3\times 2=60$.

Hence option (c) is the correct answer.