A NASCAR race has $53$ drivers racing on Sunday. How many different combinations are there for 1st, 2nd, and 3rd place?
Using combination in statistics, shouldn't the answer be $23,426$? Is this correct? ${_{53}\mathsf C}_3 = 23,426$.
2026-05-05 05:52:38.1777960358
A NASCAR race has 53 drivers racing on Sunday. How many different combinations are there for 1st, 2nd, and 3rd place?
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The order literally matters: 1st, 2nd, and 3rd place. We have 53 choices for first, then 52 for second once we've chosen 1st, and finally 51 for 3rd. Hence, we have $53\cdot 52\cdot 51 = 140556$ ways that there can be a first, second and third place.
Taking a "combination" of three drivers just counts how many groups of three you can make. It does not take into account the fact that there must be a first, second and third. If the question actually says "combination of three", then sure ${_{53}\mathsf C}_3 = 23426$.