Question

A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.

Options

• 2520.00

• 2530.00

• 2540.00

• 2550.00

Answer 1

A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be 2520.00.

Explanation:

Given 

No. of ways of selecting two husbands out of 10 = ¹⁰C₂

But their wives are to be excluded

Hence, the Remaining wives can be selected in No. of ways = ⁸C₂

But two different husbands and wives can interchange their sides in 2! ways.

∴ Required number of ways = ¹⁰C₂ × ⁸C₂ × 2!

= `10.9/2 xx 8.7/2 xx 2`

= 45 × 56

= 2520