Droupdi has 5 friends. In how many ways can she invite one or more of them to a dinner ?

Options

A. 31
B. `5^5`
C. 13
D. `2^5`

Answer

To solve the problem of how many ways Draupadi can invite one or more of her 5 friends to dinner, we can follow these steps:

### Step 1: Understand the Total Options
Each friend can either be invited or not invited. Therefore, for each of the 5 friends, there are 2 choices: invite or not invite.

### Step 2: Calculate Total Combinations
Since there are 5 friends, the total number of combinations of inviting or not inviting them can be calculated using the formula for combinations:
\[ \text{Total combinations} = 2^n \]
where \( n \) is the number of friends. Here, \( n = 5 \):
\[ 2^5 = 32 \]

### Step 3: Exclude the Case of Inviting No One
The total combinations calculated above include the scenario where Draupadi does not invite anyone at all. Since we are interested in the cases where she invites one or more friends, we need to subtract this one case from the total:
\[ \text{Ways to invite one or more friends} = 32 - 1 = 31 \]

### Final Answer
Thus, the number of ways Draupadi can invite one or more of her friends to dinner is **31**.

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