Larry has a long weekend off for 4 days that starts from Thursday and lasts till Sunday. She wants to attend some spiritual enrichment sessions that are held every day for four hours. In how many ways can she attend one or more sessions during this long weekend ?

Options

A. A) 15
B. B) 16
C. C) 4
D. D) `4 xx ^4C_1`

Answer

To solve the problem of how many ways Larry can attend one or more sessions during her long weekend, we can break it down step by step.

### Step 1: Understand the Problem
Larry has 4 days (Thursday to Sunday) and can attend a session each day. We need to find out how many different combinations of days she can choose to attend the sessions.

### Step 2: Identify the Combinations
Since Larry can attend sessions on any of the 4 days, we can represent the number of ways she can attend sessions as combinations of days. She can attend:
- 1 session
- 2 sessions
- 3 sessions
- 4 sessions

### Step 3: Calculate the Combinations
We can use the combination formula \( nCr \) which is defined as:
\[ nCr = \frac{n!}{r!(n-r)!} \]
where \( n \) is the total number of items (days in this case), and \( r \) is the number of items to choose (sessions attended).

1. **For 1 session (4C1)**:
\[ 4C1 = \frac{4!}{1!(4-1)!} = \frac{4}{1} = 4 \]

2. **For 2 sessions (4C2)**:
\[ 4C2 = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6 \]

3. **For 3 sessions (4C3)**:
\[ 4C3 = \frac{4!}{3!(4-3)!} = \frac{4}{1} = 4 \]

4. **For 4 sessions (4C4)**:
\[ 4C4 = \frac{4!}{4!(4-4)!} = 1 \]

### Step 4: Sum the Combinations
Now, we sum all the combinations calculated:
\[ 4C1 + 4C2 + 4C3 + 4C4 = 4 + 6 + 4 + 1 = 15 \]

### Final Answer
Thus, the total number of ways Larry can attend one or more sessions during her long weekend is **15**.

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