Question

If the number of ways in which a mixed double badminton can be played such that no couples played into a same game is 840. Then find the number of players?

Answer 1

Let the number of couples be \( n \).

The total number of ways is given by:

\( \frac{n(n-1)}{2} \cdot \frac{(n-2)(n-3)}{2} \cdot 2 = 840 \).

Step 1: Simplify the equation:

\( n(n-1)(n-2)(n-3) = 840 \cdot 4 \).

\( n(n-1)(n-2)(n-3) = 3360 \).

Step 2: Factorize \( 3360 \):

\( 3360 = 8 \cdot 7 \cdot 6 \cdot 5 \).

Thus, \( n = 8 \).

Step 3: Calculate the total number of persons:

Total persons = \( 2n = 2(8) = 16 \).

Final Answer: The number of persons is \( 16 \).

Answer 2

Let total number of couples be n
According to given condition,

\(\therefore\) Total players = \(8\times 2\) = 16