Question

There are 32 tennis players participating in a tournament. How many ways are there to select a top 3 (not distinguishing between first, second, and third place finishes)

Answer 1

To select a top 3 from 32 tennis players, we use the combination formula 32C3, which results in 4,960 different ways to make the selection.

Step-by-step explanation:

To find the number of ways to select a top 3 from 32 tennis players without distinguishing between first, second, and third places, we use the combination formula.

Since the order does not matter, we are dealing with combinations and not permutations.

The number of ways to choose 3 players out of 32 is given by the combination formula which is 32C3 (32 choose 3).

The combination formula is:

nCr = n! / (r!(n-r)!),

where n is the total number of items, r is the number of items to choose, and ! denotes factorial. So for our case, it would be:

32C3 = 32! / (3!(32-3)!)

Calculating this yields:

32! / (3! × 29!) = (32 × 31 × 30) / (3 × 2 × 1) = 4960 way

Therefore, there are 4,960 different ways to select a top 3 from 32 tennis players.