Introduction:
Scarcity refers to the limited availability of resources in relation to unlimited wants and needs. It is a fundamental concept in economics as it necessitates the allocation of resources to satisfy the most pressing needs. In this context, we will analyze the given options to determine if any economy is without scarcity.

Analysis:
a) The pre-independence Indian economy, where most people were farmers:
In the pre-independence Indian economy, the majority of the population were engaged in agriculture as farmers. While they had access to land and resources for cultivation, scarcity still existed. Farmers faced limitations in terms of land, water, fertilizers, and other inputs necessary for agricultural production. Additionally, they also had limited access to markets and faced challenges in securing fair prices for their produce. Therefore, scarcity was prevalent in the pre-independence Indian economy.

b) A mythical economy where everybody is a billionaire:
In a mythical economy where everybody is a billionaire, scarcity may appear to be eliminated at first glance. However, scarcity is not solely determined by the availability of wealth. It is also influenced by the availability of resources and the allocation of goods and services. Even if everyone is a billionaire, there will still be a limited supply of resources such as land, labor, capital, and natural resources. Moreover, the allocation of goods and services will require choices and trade-offs, as individuals' wants and needs will still surpass the available resources. Therefore, even in such a mythical economy, scarcity would still exist.

c) Any economy where income is distributed equally among its people:
In an economy where income is distributed equally among its people, scarcity would still prevail. While equal distribution of income may contribute to reducing inequality, it does not eliminate the limited availability of resources. Scarce resources such as land, labor, and capital would still need to be allocated efficiently to meet the needs and wants of the population. Moreover, individuals' preferences and demands vary, which would require choices and trade-offs to be made in resource allocation. Consequently, scarcity would persist in any economy, irrespective of income distribution.

Conclusion:
After analyzing the given options, it is evident that none of the economies mentioned are without scarcity. Scarcity arises due to the limited availability of resources relative to unlimited wants and needs. It is a core economic concept that necessitates the allocation of resources to satisfy the most pressing needs. While different economic systems and income distributions can influence the degree of scarcity, it cannot be entirely eliminated.