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Eight players are to be split into 4 pairs for a doubles badminton practice. In how many ways can the pairs be formed?

Competition practicePermutations & Combinations

A2520
B420
C105
D35

Step-by-Step Solution

Labelled pairs would give

\frac{8 !}{( 2 ! ) ^{4}} = 2520

. The 4 pairs carry no names, so divide by

4! : 2520 \div 24 = 105

. Another way:

7 \times 5 \times 3 \times 1 = 105

.

Answer: C) 105

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