A person is permitted to select at least one and at most coins from a collection of distinct coins. If the total number of ways in which he can select coins is , then equals?
Explanation for the correct option:
Step 1: Express an equation for the given situation:
Given: Number of ways of selecting one to coins from a collection of distinct coins, is
In mathematical terms, It can be expressed as follows:
Step 2: Find the sum of the obtained expression:
Use Binomial coefficients relation to find the sum.
Step 3: Put the given value and simplify the equation:
Put the given value of the sum in the obtained expression.
Hence, option (A) is the correct answer.